This paper presents the singularity analysis of four 3-DOF symmetric zero-torsion parallel mechanisms. These mechanisms are composed of three identical legs ending with a spherical joint that is constrained to move in one of three equally spaced plane intersecting at one line. The computation of the singularity loci is based on the degeneracy of the system of screws applied on the platform by the legs. The whole study is based on the use of a special orientation representation, previously introduced under the name of Tilt-and-Torsion angles. This representation is briefly introduced. Then the interdependence between the Cartesian coordinates of the general class of parallel mechanisms is derived. Finally, the singularity loci are derived and the size of the workspace taking into account all singular configurations is shown.

I. INTRODUCTION

OR the last few decades, parallel mechanisms are increasingly being used and studied. Even if most works on parallel mechanisms were focused on 6-degrees-offreedom (DOFs) mechanisms (mainly hexapods), recently, more interest has been paid to mechanisms with less than 6 DOFs. The most popular of these mechanisms belong undoubtedly to the group of 3-DOF symmetric parallel mechanisms whose mobile platform is attached to three identical legs via spherical joints (Fig. 1). The legs constrain the centers of the spherical joints to move in three equally spaced vertical planes intersecting at a common line. These mechanisms will be referred to as 3-[PP]S ones 1 .

There is abundant literature on this group of mechanisms, studying their kinematics, singularity analysis and design. For example, a 3-PPS parallel mechanism was proposed in [START_REF] Liu | A new 3-DoF parallel mechanism with full symmetrical structure and parasitic motions[END_REF] (Fig. 1a), the 3-RPS architecture (Fig. 1b) was analyzed in [START_REF] Lee | Kinematic analysis of a three-degreeoffreedom in-parallel actuated manipulator[END_REF][START_REF] Buruncuk | On the kinematics of a 3-DOF Stewart platform[END_REF][START_REF] Kim | Kinematic synthesis of a spatial 3-RPS parallel manipulator[END_REF][START_REF] Liu | Direct singular positions of 3RPS parallel manipulators[END_REF][START_REF] Sokolov | Singularity analysis of a 3-DOF parallel manipulator with R-P-S joint structure[END_REF], two different 3-PRS designs were studied in [START_REF] Carretero | Workspace analysis and optimization of a novel 3-DOF parallel manipulator[END_REF] (Fig. 1c) and [START_REF] Tsai | Direct kinematic analysis of a 3-PRS parallel mechanism[END_REF] (Fig. 1d), the latter design being best known through the Z3 Head by DS Technologie [START_REF] Wahl | Articulated tool head[END_REF], and finally a 3-RRS robot was investigated in [START_REF] Li | Inverse kinematics and dynamics of the 3-RRS parallel platform[END_REF]. Of all these publications, only [START_REF] Buruncuk | On the kinematics of a 3-DOF Stewart platform[END_REF] seems to identify the exact nature of the interdependence of the orientation parameters and its geometric significance. To fill this important gap, the second author studied the kinematic geometry of 3-[PP]S parallel mechanisms and showed clearly their motion pattern [START_REF] Bonev | Advantages of the modified Euler angles in the design and control of PKMs[END_REF].

Manuscript received January 25, 2008. This work was supported by FQRNT and the French Ministère des Affaires étrangères et européennes.

Sébastien Briot and I.A. Bonev are with the Department of Automated Manufacturing Engineering of the École de technologie supérieure (ÉTS), Montreal, QC, Canada H3C 1K3 (phone: 514-396-8403; fax: 514-396-8595; e-mails: sebastien.briot.1@ens.etsmtl.ca, ilian.bonev@etsmtl.ca). 1 It is common to denote parallel mechanisms by using the symbols P, R, and S, which stand respectively for prismatic, revolute and spherical joint. When a joint is actuated, its symbol is underlined. In this paper, we also use [PP] to denote any combination of joints that allows 2-DOF planar motion. In this paper, we use a special orientation representation to obtain simplified relations for the singularity analysis of these mechanisms. This orientation representation was recently applied to the derivation of the closed-form direct kinematics of the mechanisms shown in Fig. 1(a-c) [START_REF] Bonev | Direct kinematics of zero-torsion parallel mechanisms[END_REF]. It was shown that this representation considerably simplify the expressions of the direct kinematics of such mechanisms. Thus, in the next section, we describe briefly this orientation representation and use it in Section 3 to derive the simple interdependence between the orientation angles and the position of the platform of a general 3-[PP]S parallel mechanism. Then, in Section 4, we present the expression of the singularity loci of four 3-[PP]S parallel mechanisms, namely the 3-PPS design (Fig. 1a), the general 3-RPS design (Fig. 1b), and two common 3-PRS designs (Fig. 1c and1d).

We also analyze the size of the singularity-free workspace of these structures, as a function of the design parameters, taking into account all singular configurations. Finally, conclusions are drawn in Section 5.

Singularity Analysis of Zero-Torsion Parallel Mechanisms

Sébastien Briot and Ilian A. Bonev, Member, IEEE F Fig. 2. The successive rotations of the T&T angles: (a) tilt, (b) torsion II. ORIENTATION REPRESENTATION A novel three-angle orientation representation, later called the Tilt-and-Torsion (T&T) angles, was proposed in [START_REF] Bonev | Orientation workspace analysis of 6-DOF parallel manipulators[END_REF] in 1999, in conjunction with a new method for computing the orientation workspace of symmetric spatial parallel mechanisms. It was shown that the T&T angles take full advantage of a mechanism's symmetry. These angles were also independently introduced in [START_REF] Huang | Closed form solution to workspace of hexapod-based virtual axis machine tools[END_REF] and [START_REF] Wang | Workspace analysis of a novel closed-chain manipulator[END_REF] in 1999. Later, it was found out that the angles had been proposed in [START_REF] Korein | A Geometric Investigation of Reach[END_REF] in 1984 under the name halfplane-deviation-twist angles. The author of that reference proposed the set due to its indisputable advantages in modeling the limits of human body joints. Yet, again in 1999, these angles were proposed independently in [START_REF] Crawford | A new technique for determining 3-D joint angles: The tilt/twist method[END_REF] as a new standard in modeling angular joint motion, and particularly that of the spinal column's vertebra. These angles are also used for computer animation of articulated bodies, known as the swing-and-twist representation. In [START_REF] Bonev | Advantages of the modified Euler angles in the design and control of PKMs[END_REF], the advantages of the T&T angles in the study of spatial parallel mechanisms were further demonstrated. It was shown that there is a class of 3-DOF mechanisms that have always a zero torsion, that we now call zero-torsion parallel mechanisms. Furthermore, it was demonstrated in [START_REF] Bonev | Singularity loci of spherical parallel mechanisms[END_REF] and [START_REF] Bonev | Analytical determination of the workspace of symmetrical spherical parallel mechanisms[END_REF] that the workspace and singularities of symmetric spherical parallel mechanisms are best analyzed using the T&T angles.

The T&T angles are defined in two stages-a tilt and a torsion. This does not, however, mean that only two angles define the T&T angles but simply that the axis of tilt is variable and is defined by another angle. In the first stage, illustrated in Fig. 2a, the body frame is tilted about a horizontal axis, a, at an angle θ, referred to as the tilt. The axis a is defined by an angle φ, called the azimuth, which is the angle between the projection of the body z' axis onto the fixed xy plane and the fixed x axis. In the second stage, illustrated in Fig. 2b, the body frame is rotated about the body z' axis at an angle σ, called the torsion.

For space limitations, we will omit the otherwise quite interesting details of the derivation process (see [START_REF] Bonev | Advantages of the modified Euler angles in the design and control of PKMs[END_REF]), and write directly the resulting rotation matrix of the T&T angles, which is

          - + - + - - - = - - - - - - - - - - θ φ σ θ φ σ θ θ φ φ σ φ φ σ θ φ φ σ φ φ σ θ φ θ φ φ σ φ φ σ θ φ φ σ φ φ σ θ φ σ θ φ c s s c s s s c c s c s s c c c s s c c s s c c s s c c c ) , , ( R , ( 1
)
where c φ = cos φ, s φ = sin φ, c θ = cos θ, s θ = sin θ, c σ-φ = cos(σ-φ) and s σ-φ = sin(σ-φ).

One of the properties of three-angle orientation representation is that a given orientation can be represented by at least two triplets of angles. In our case, the triplets {φ, θ, σ} and {φ ± π, -θ, σ} are equivalent. To avoid this and the representational singularity at θ = π (which is hardly achieved by any parallel mechanism), we set the ranges of the azimuth, tilt, and torsion as, respectively, φ ∈ (-π; π], θ ∈ [0, π), and σ ∈ (-π; π]. Then, probably the most valuable property of the T&T angles is that for the ranges just defined, the angles (φ, θ, σ) can be represented in a cylindrical coordinate system (r, φ, h) through a one-to-one mapping. In other words, any orientation (except a θ = π one) corresponds to a unique point within a cylinder in the cylindrical coordinate system, and vice versa. The reason is that the T&T representational singularity at θ = 0 is of the same nature as the singularity of the cylindrical coordinate system occurring at zero-radius (r = 0).

III. KINEMATIC GEOMETRY OF 3-[PP]S PARALLEL MECHANISMS

As already mentioned, each leg of a 3-[PP]S parallel mechanisms has a 2-DOF planar chain, followed by an S joint. The vertical planes in which the three equidistant S joints move are intersecting at a common line at 120° (Fig. 3). Now, let O -xyz be the base reference frame, such that its z axis coincides with the common line of the three planes, and its x axis lies in the plane of leg 1.

For brevity, let the three equidistant S joint centers, denoted by B i , lie on a circle of radius 1, i.e.,

T CB ] 0 , 0 , 1 [ ' 1 = r , (2)
T CB ] 0 ), 3 / 2 sin( ), 3 / 2 [cos( ' 2 π π = r , ( 3
) T CB ] 0 ), 3 / 4 sin( ), 3 / 4 [cos( ' 3 π π = r , (4)
where r' CBi are the vectors along CB i expressed in the mobile frame C -x'y'z'. We, then, express the coordinates of these three points in terms of the coordinates of the platform center, x, y, z, and the three T&T angles:

          =           + = i i i i i OB OB OB OB OB z y x z y x ' r R r , ( 5
)
where R is the rotation matrix defined by (1) (in this paper, i = 1, 2, 3). Then, we write the three linear equations that constrain the S joint centers in the three vertical planes:

0 1 = OB y , (6) 0
) 3 / 2 sin( ) 3 / 2 cos( 2 2 = - OB OB x y π π , ( 7
) 0 ) 3 / 4 sin( ) 3 / 4 cos( 3 3 = - OB OB x y π π , ( 8
)
Since z is obviously an independent coordinate, it is of no surprise that, after substitution of y OB1 , x OB2 , y OB2 , x OB3 , and y OB3 from (5), none of the above three equations contains that variable:

0 3 , 1 = + q y , ( 9
) 0 2 1 2 3 3 , 2 = + - - q y x , (10) 0 2 1 2 3 3
, 3 = + - q y x , (11)
where q 1,3 , q 2,3 , and q 3,3 are functions of the three T&T angles. Therefore, in order to have a solution for x and y, the three linear equations must be linearly dependent. Obviously, any two of these equations are linearly independent. Hence, for any feasible orientation of the mobile platform, there is a unique solution for {x, y}.

Let Q be the coefficient matrix for the above three equations, i.e., 1,3

2,3 3,3 0 1 3 1 2 2 3 1 2 2 q q q       = - -       -     Q . ( 12
)
For these equations to be linearly dependent, the matrix Q should be singular, i.e.,

(

)

0 1 cos sin 4 3 3 det = + = θ σ Q . ( 13
)
Disregarding θ = π, (13) leads us to the only remaining possibility: σ = 0 or σ = π. If we substitute σ = 0 or σ = π in [START_REF] Wahl | Articulated tool head[END_REF][START_REF] Li | Inverse kinematics and dynamics of the 3-RRS parallel platform[END_REF][START_REF] Bonev | Advantages of the modified Euler angles in the design and control of PKMs[END_REF], and solve any two of them, we obtain the following for the feasible motion of the mobile platform center:

( )

1 cos 2 cos 2 1 δ - = θ φ x , (14)
( )

1 cos 2 sin 2 1 δ - - = θ φ y , (15)
where δ = 1 for σ = 0 and δ = -1 for σ = π. These two modes of operation are separated by a constraint singularity, which occurs at θ = 0. Indeed, as shown in [START_REF] Zlatanov | Constraint singularities of parallel mechanisms[END_REF], constraint singularities generally separate the different modes of operation of constrained parallel mechanisms. While both modes exist in theory, in practice the tilt angle θ will be quite limited, and the actual prototype will be confined to operate in only one of the modes. Furthermore, in practice, the mode σ = π is hardly realizable. Therefore, for any practical

IV. SINGULARITY LOCI OF 3-[PP]S PARALLEL MECHANISMS

Among the abundant literature devoted to 3-[PP]S mechanisms, only a few papers deal with the subject of singularities [START_REF] Liu | Direct singular positions of 3RPS parallel manipulators[END_REF][START_REF] Sokolov | Singularity analysis of a 3-DOF parallel manipulator with R-P-S joint structure[END_REF][START_REF] Pond | Singularity analysis and workspace optimization of the inclined PRS manipulator[END_REF][START_REF] Ebert-Uphoff | Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs[END_REF]. Among these papers, references [START_REF] Liu | Direct singular positions of 3RPS parallel manipulators[END_REF][START_REF] Sokolov | Singularity analysis of a 3-DOF parallel manipulator with R-P-S joint structure[END_REF] present the singularity analysis of a 3-RPS structure. However, in both papers, the obtained expressions are numerous and complicated due to the use of general Euler angles and are basically not exploitable. Reference [START_REF] Pond | Singularity analysis and workspace optimization of the inclined PRS manipulator[END_REF] presents a short singularity analysis of the 3-PRS structure, but gives no expressions characterizing the singular configurations. Finally, reference [START_REF] Ebert-Uphoff | Characteristic tetrahedron of wrench singularities for parallel manipulators with three legs[END_REF] presents a geometric approach to finding Type 2 singularities of three-legged parallel mechanisms.

In this section, we will analyze the Type 2 singularities of four 3-[PP]S parallel mechanisms, namely the 3-PPS design, proposed in [START_REF] Liu | A new 3-DoF parallel mechanism with full symmetrical structure and parasitic motions[END_REF] (Fig. 1a), the general 3-RPS design (Fig. 1b), and the two 3-PRS designs proposed in [START_REF] Carretero | Workspace analysis and optimization of a novel 3-DOF parallel manipulator[END_REF] and [START_REF] Tsai | Direct kinematic analysis of a 3-PRS parallel mechanism[END_REF] (Fig. 1c and1d). To realize this analysis, we will study the degeneracy of a 6-dimensional matrix composed of the screws applied on the platform by the moving legs and will give for the first two mechanisms (the 3-PPS and the 3-RPS) simple analytical expressions characterizing the singularity loci obtained by the use of the T&T angles. We will show for the other two mechanisms that the singularity loci can be represented by a polynomial of high order (of degree 24). Moreover, for each mechanism, the maximal reachable workspace taking into account the singular configuration will be represented as a function of the design parameters.

A. Singularity Loci of 3-PPS Parallel Mechanisms

Referring to Fig. 4, the directions of the actuated prismatic joints are vertical, while the directions of the passive prismatic joints are horizontal.

Each leg applied two screws R i1 and R i2 on the platform. Thus, as shown on Fig. 4, for this manipulator, R i1 and R i2 are two forces located at point B i and directed along the vertical axis z and perpendicular to the plane of the legs, respectively. The system of screws degenerates if the determinant of matrix J, of which the lines are composed of the coordinates of the screws R ij (j = 1, 2), vanishes. After simplification, this determinant can be written as: The approach used to compute the maximal reachable angle θ can be described as follows. First, we fix the design parameter R b and discretize the variable space {z, φ, θ}. Then, for a given set of variables {z, φ} and starting from θ = 0, we observe the evolution of the sign of the determinant of matrix J when θ is varying. We met a singularity if, between two values of θ, the sign of det J varies. Thus, we stop the procedure and retain the value θ m of angle θ just before crossing the singular configuration. Then, we redo this algorithm for another value of angle φ. When this procedure has been realized for any angle φ, we find the minima of the angles θ m , plot it on Fig. 7 and execute another time the entire algorithm.

( ) θ θ cos 1 cos 8 27 det + = J , (17)
Thus, it can be observed that the size of the workspace increases with the altitude of the platform and decrease with the value of R b .

C. Singularity Loci of 3-RPS Parallel Mechanisms

As for the previous mechanism, R i1 and R i2 are two forces located at point B i , the first directed along the direction of the leg and the second perpendicular to the plane of the legs. The system of screws degenerates if:

Fig. 1 .

 1 Fig. 1. Examples of 3-DOF 3-[PP]S parallel mechanisms

Fig. 3 .

 3 Fig. 3. Kinematic geometry of a general 3-[PP]S parallel mechanism

3 -

 3 [PP]S parallel mechanism, σ = 0. Let us now analyze the singularity loci of several examples of 3-[PP]S parallel mechanisms.

Fig. 4 .

 4 Fig. 4. Schematics of a 3-PPS parallel mechanism Disregarding θ = π, (13) leads us to the only remaining possibility for Type 2 singularities: θ = ±π/2.Thus, for any 3-PPS parallel manipulator, the workspace is bounded by the orientation θ = ±π/2 of the platform, for any altitude z and angle φ.

B

  . Singularity Loci of 3-RPS Parallel MechanismsAs shown in Fig.5, for this mechanism, R i1 and R i2 are two forces located at point B i , the first directed along the line A i B i and the second perpendicular to the plane of the legs. The system of screws degenerates if: c 0 , c 1 and c 2 depend on angle θ, on the altitude z of the center of the platform and on the radius R b of the circumcircle of the base, is quite simple to find the exact expression of the singularity loci expressing angle φ as a function of the other parameters:

Fig. 6

 6 Fig.6shows an example of singularity loci in the workspace of a 3-RPS parallel mechanism with R b = 1.3 for z = 1. We can now analyze the size of the workspace represented by the maximal reachable angle θ for any angle φ as a function of the altitude of the platform and of the design parameters R b (Fig.7).

Fig. 5 .Fig. 6 . 1 Fig. 7 .

 5617 Fig. 5. Schematics of a 3-RPS parallel mechanism

In these expressions, Γ i and ∆ i are radicals depending on the working mode (solution of the inverse kinematics) of the mechanism. Thus, Type 2 singularity loci are much more complicated to determine due to the existence of these terms.

Indeed, to eliminate all radicals in the equation det J, the latter should be rearranged and squared three times, using a similar method as that proposed in [START_REF] Bonev | Singularity Loci of Planar Parallel Manipulators with Revolute Joints[END_REF] for the 3-RRR planar parallel robot. The equation resulting after these operations corresponds to all eight working modes.

Since this procedure cannot be performed symbolically, we firstly assign random integer values to the coefficients θ, R b , L, and z. Then, we eliminate the radicals by rearranging terms and squaring three times the equations. Finally, as the system is symmetrical, it is possible to rearrange the obtained polynomial in cos φ and sin φ into a polynomial in cos 3φ.

Finally, it can be observed that the obtained polynomials are of degree 16 for the mechanism of Fig. 1c, and of degree 24 for the mechanism of Fig. 1d. Fig. 8 shows examples of singularity loci in the workspace of the 3-PRS parallel mechanisms under study.

Finally, we analyze the size of the singularity-free workspace represented by the minimum of all maximal reachable angles θ for any angle φ, without reaching a singularity, as a function of the altitude of the platform and of the design parameters R b and L (Fig. 9a and9b). We use an algorithm similar to that used for the 3-RPS parallel mechanism. It can be observed that:

-for the mechanism of Fig. 1c, the size of the singularity-free workspace increases with the altitude of the platform; moreover, for L close to 2 and for a high altitude z, the value of angle θ reaches 90°.

-for the mechanism of Fig. 1d, the size of the singularity-free workspace increases when L increase and R b decrease; moreover, for R b close to 1, the value of angle θ reaches 80°.

V. CONCLUSIONS

We presented in this paper yet another example of the advantages of using Tilt-and-Torsion angles for the analysis of 3-DOF zero-torsion parallel mechanisms. In particular, we proposed, for the first time, simple expressions for the singular configurations of four different zero-torsion mechanisms, namely a 3-PPS design, the general 3-RPS design, and two 3-PRS design. Furthermore, we analyzed the maximal singularity-free workspace of these mechanisms as a function of their design parameters. It should now be clear that so-called zero-torsion parallel mechanisms must be analyzed using Tilt-and-Torsion angles only.


Sebastien Briot

Vigen Arakelian

ON THE KINEMATIC, KINETOSTATIC AND DYNAMIC PROPERTIES OF PARALLEL MANIPULATORS IN THE PRESENCE OF SINGULARITY

Introduction

Over the past decades, with the large development of parallel structures, more attention has been paid to their kinematic, kinetostatic and dynamic properties, and in particular, to their singularities. Several papers deal with singularity analysis of parallel manipulators [START_REF] Gosselin | Singularity Analysis of Closed-Loop Kinematic Chains[END_REF][START_REF] Zlatanov | Singularity Analysis of Mechanisms and Robots via a Velocity-Equation Model of the Instantaneous Kinematics[END_REF][START_REF] Zlatanov | Constraint Singularities of Parallel Mechanisms[END_REF][START_REF] Merlet | Singular Configurations of Parallel Manipulators and Grassmann Geometry[END_REF][START_REF] Bonev | Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory[END_REF][START_REF] Gosselin | The Optimum Design of Robotic Manipulators using Dexterity Indices[END_REF][START_REF] Merlet | Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots[END_REF][START_REF] Angeles | Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms[END_REF][START_REF] Nenchev | Dynamic Analysis of Parallel Manipulator under the Singularity-Consistent Parameterization[END_REF][START_REF] Ider | Inverse Dynamics of Parallel Manipulators in the Presence of Drive Singularities[END_REF][START_REF] Maass | Control Strategies for Elarging a Spatial Robot's Workspace by Change of Configuration[END_REF]. Most of them present the analysis of singular configurations from a kinematic point of view [START_REF] Gosselin | Singularity Analysis of Closed-Loop Kinematic Chains[END_REF][START_REF] Zlatanov | Singularity Analysis of Mechanisms and Robots via a Velocity-Equation Model of the Instantaneous Kinematics[END_REF][START_REF] Zlatanov | Constraint Singularities of Parallel Mechanisms[END_REF][START_REF] Merlet | Singular Configurations of Parallel Manipulators and Grassmann Geometry[END_REF][START_REF] Bonev | Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory[END_REF]. Algebraically, a singularity analysis is based on the degeneracy of Jacobian matrices of the mechanical structure, or of the system of reciprocal screws (wrenches) applied to the platform by the legs. However, it is also known that, when parallel manipulators have Type 2 singularities [START_REF] Gosselin | Singularity Analysis of Closed-Loop Kinematic Chains[END_REF], they lose their stiffness and their quality of motion transmission, as a result, their payload capability. Therefore, the singularity zones in the workspace of manipulators may be analysed not only in terms of kinematic criterions, from the theoretically perfect model of manipulators, but also in terms of kinetostatic approaches [START_REF] Gosselin | The Optimum Design of Robotic Manipulators using Dexterity Indices[END_REF][START_REF] Merlet | Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots[END_REF][START_REF] Angeles | Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms[END_REF]. However, the proposed criterions are difficult to use, above all when applied to manipulators involving both translational and rotational degrees of freedom (DOF).

Moreover, while it is demonstrated using the kinetostatic approach that, when subjected to Type 2 singularities parallel manipulator lock up, it has been shown experimentally that, via optimal dynamic control of manipulators, it is possible to pass through these singular zones [START_REF] Nenchev | Dynamic Analysis of Parallel Manipulator under the Singularity-Consistent Parameterization[END_REF][START_REF] Ider | Inverse Dynamics of Parallel Manipulators in the Presence of Drive Singularities[END_REF][START_REF] Maass | Control Strategies for Elarging a Spatial Robot's Workspace by Change of Configuration[END_REF]. Thus, singular configurations should also be examined in terms of dynamic aspects.

In this paper, we present an overview of our recent works on the kinematic, kinetostatic and dynamic aspects of singularities. As an application of our works, the singular configurations of a new manipulator developed at the INSA of Rennes (PAMINSA: PArallel Manipulator of the INSA [START_REF] Briot | PAMINSA: a New Family of Partially Decoupled Parallel Manipulators[END_REF]) are studied from kinematic, kinetostatic and dynamic points of Sébastien Briot, Vigen Arakelian, 20 avenue des buttes de Coësmes, CS 14315, 35043 Rennes Cedex -France, Phone : +33 2 23 23 84 92, Fax : +33 2 23 23 87 26, vigen.arakelyan@insarennes.fr view. This paper is divided up as follows. The following section presents the kinematic analysis of singularity in more detail, and a brief review of previous works on this topic is carried out. Then, a kinetostatic analysis is performed. For this purpose, the pressure angle is used as a kinetostatic indicator of force transmission. Finally, we present the optimal dynamic conditions generating stable motions inside the singular zones. To obtain a demonstration of the mentioned properties, experimentations are performed on a prototype of PAMINSA.

Kinematic analysis of singular configurations

The singularities are defined in [START_REF] Gosselin | Singularity Analysis of Closed-Loop Kinematic Chains[END_REF] as configurations of manipulators where the platform may instantaneously lose (Type 1 singularities) or gain (Type 2 singularities or also constraint singularities [START_REF] Zlatanov | Constraint Singularities of Parallel Mechanisms[END_REF]) one (or more) DOF. From the kinematic point of view, several methods can be used in order to find the singularity loci of a manipulator, or to interpret the kinematic meaning of such configurations. These methods can be classified into two different classes: -algebraic approaches, such as the study of the degeneracy of the Jacobian matrices of the mechanical structure, or of the system of reciprocal screws (wrenches) applied to the platform by the legs [START_REF] Gosselin | Singularity Analysis of Closed-Loop Kinematic Chains[END_REF][START_REF] Zlatanov | Singularity Analysis of Mechanisms and Robots via a Velocity-Equation Model of the Instantaneous Kinematics[END_REF][START_REF] Zlatanov | Constraint Singularities of Parallel Mechanisms[END_REF]. -geometric approaches, such as analyses using screw theory, Grassman geometry [START_REF] Merlet | Singular Configurations of Parallel Manipulators and Grassmann Geometry[END_REF][START_REF] Bonev | Singularity Analysis of 3-DOF Planar Parallel Mechanisms via Screw Theory[END_REF]; Each of these methods enable us to find, symbolically or numerically, the singularity loci of parallel mechanisms and to analyse the behaviour of the manipulator in such configurations. However, they are able to define the exact loci of singularities only when taking into account the perfect theoretical model of the mechanism and do not enable us to analyze the loss of functionality of the manipulator in the domain of singular configurations. For such a study, it is necessary to carry out a kinetostatic analysis of the singular configuration. This will be developed in the next section. Firstly, we would like to present an example of the application of the kinematic analysis of singularities on the PAMINSA manipulator (Fig. 1). The PAMINSA is a manipulator which performs Shoenflies motions. It belongs to a new family of partially decoupled parallel robots having between three and six DOF which was recently developed at the INSA of Rennes (France). The particularity of the PAMINSA is the decoupling of the displacements of the platform in the horizontal plane from the translations along the vertical axis. In order to understand the remainder of the paper, it is of utmost importance to take into account that, due to its decoupling properties, the kinematic model for the planar displacement of the PAMINSA is equivalent to a planar parallel 3-RPR robot, with the first revolute joints actuated. For further information, we advise the reader to refer to [START_REF] Briot | PAMINSA: a New Family of Partially Decoupled Parallel Manipulators[END_REF].

In [START_REF] Briot | PAMINSA: a New Family of Partially Decoupled Parallel Manipulators[END_REF][START_REF] Arakelian | Singular Position of a PAMINSA Parallel Manipulator[END_REF][START_REF] Briot | Self Motions of General 3-RPR Planar Parallel Robots[END_REF], the singular configurations of the PAMINSA are analysed in terms of kinematic aspects, via both geometric and algebraic approaches. In these papers, it is shown that Type 1 singularities appear when:

points A i , B i and C i of manipulator's legs are aligned along a vertical axis (Fig. 2a); in such a case, the leg actuated in rotation about the vertical axis does not produce a displacement of the platform; -the parallelogram A i F i D i E i degenerates into a line.

The Type 2 singular configurations appear when: -the orientation angle  of the platform around the vertical axis is equal to ) / ( cos 1

 cos 2 2 2 i i i i OO PC OO PC  
; in such a case, the platform gains a rotation around a vertical axis passing through point W (Fig. 2b) and perform a Cardanic self motion [START_REF] Briot | Self Motions of General 3-RPR Planar Parallel Robots[END_REF].

Let us now deal with the kinetostatic aspects of singular configurations.

Kinetostatic analysis of singular configurations

It is well known that, when parallel manipulators are close to Type 2 singularities, they lose their stiffness along with their quality of motion transmission, and as a result, their payload capability. Therefore, the singularity zones in the workspace of manipulators cannot be defined by kinematic criterions only, from the theoretical perfect model of manipulators, but must also take into account kinetostatic approaches.

The most common indices used to characterize the loss of the quality of motion transmission are conditioning or dexterity indices [START_REF] Gosselin | The Optimum Design of Robotic Manipulators using Dexterity Indices[END_REF][START_REF] Merlet | Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots[END_REF][START_REF] Angeles | Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms[END_REF]. However, as pointed out in [START_REF] Merlet | Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots[END_REF], the major drawbacks of these concepts are that they mix arbitrary translational and rotational capabilities and that they usually do not enable a variation in the choice of units. Therefore, we propose using another index, which, contrary to the previous ones, is invariant and has a strong physical meaning: the pressure angle [START_REF] Balli | Transmission Angle in Mechanisms[END_REF][START_REF] Arakelian | Increase of Singularity-Free Zones in the Workspace of Parallel Manipulators Using Mechanisms of Variable Structure[END_REF]. It will be used as a kinetostatic indicator of force transmission and may characterize the "distance" of the mechanism from the Type 2 singularity.

For a parallel mechanism with n legs, the pressure angle is defined as the angle between the force F applied by the leg i (i = 1 to n) to the platform at point C i and the passive velocity of the platform at the same point, when the actuator of leg i is disconnected. Therefore, for such a mechanism, n pressure angles exist. It could be proved that, when the platform is subject to Type 2 singularities, the value of the pressure angle is equal to 90°. On the contrary, when the manipulator is at an isotropic configuration, the pressure angle is equal to 0°. Therefore, it is preferable to have a mechanism of which the maximal values of the pressure angles inside its workspace is as close as possible to 0°.

Let us examine the pressure angle of the PAMINSA. In the absence of a gravity field, and due to its decoupling properties, its pressure angle is completely equivalent to that of the 3-RPR mechanism. Thus, the pressure angle  1 of leg 1 is defined as the angle between the force R 1 applied by the leg 1 to the platform and the passive velocity of the platform V C1 when leg 1 is disconnected (Fig. 3a). For more detailed explanations on the calculation of angle  1 , please refer to [START_REF] Arakelian | Increase of Singularity-Free Zones in the Workspace of Parallel Manipulators Using Mechanisms of Variable Structure[END_REF]. As the mechanism has three legs, three pressure angles ( 1 ,  2 ,  3 ) can be derived by the same approach. The kinetostatic criterion we propose to use is  m = max( 1 ,  2 ,  3 ) (Fig. 3b). In Fig. 3b, the black zones are the surfaces where the pressure angle has inadmissible values, and as a result these are the zones in which the parallel mechanism may block. However, it is possible to mention that the locking of the mechanism may be avoided if the system of wrenches applied to the mechanism complies with the condition presented in the next section.

Dynamic analysis of singular configurations

While it is demonstrated using the kinetostatic approach that subject to Type 2 singularities a parallel manipulator locks up, it has been shown experimentally that via optimal dynamic control of manipulators it is possible to pass through these singular zones [START_REF] Nenchev | Dynamic Analysis of Parallel Manipulator under the Singularity-Consistent Parameterization[END_REF][START_REF] Ider | Inverse Dynamics of Parallel Manipulators in the Presence of Drive Singularities[END_REF][START_REF] Maass | Control Strategies for Elarging a Spatial Robot's Workspace by Change of Configuration[END_REF]. Thus, singular configurations should also be examined in terms of dynamic aspects.

In [START_REF] Briot | On the Dynamic Properties and Optimum Control of Parallel Manipulators in the Presence of Singularity[END_REF], we have determined the optimal dynamic conditions generating stable motions inside the singular zones. The obtained results show that the general conditions for passing through singularities can be defined as: the end-effector being able to pass through the singularity without perturbation of motion if the wrench applied to the end-effector by the legs and external efforts is orthogonal to the twist along the direction of the uncontrollable motion. This condition is obtained via inverse dynamics and derived in the example of the PAMINSA manipulator.

For validating this condition, we have carried out experimental tests on the prototype of PAMINSA (Fig. 1b). We have applied an arbitrary fifth order control law and observed the reproduction of motion during the displacement of the platform. The obtained trajectory is shown in Fig. 4 (dashed line). The circle in dotted line corresponds to the singularity loci. The different positions are classified in terms of time. For positions from (a) to (d), the platform moves towards the singular zone yet remains outside of it. In this case, the reproduction of the real trajectory is similar to that sought after. At position (e), the manipulator enters the singular zone, which is close to the circle of the theoretical singular loci, and starts an uncontrollable motion. Thus, since the motion generation is carried out by non optimized dynamic parameters, the platform moves along an unplanned trajectory (see positions (e) -(h) in Fig. 8).

Next, we have implemented a trajectory which makes it possible to comply with the previous condition and have observed the behaviour of the platform during the displacement. While not shown here, during each displacement, the manipulator retains its orientation constant and passes through the singular configuration without any perturbation. For more detailed information, the reader should refer to [START_REF] Briot | On the Dynamic Properties and Optimum Control of Parallel Manipulators in the Presence of Singularity[END_REF].

Conclusions

In this paper, we have presented an overview of our recent works on the kinematic, kinetostatic and dynamic aspects of singularities. As an application of our works, the singular configurations of a new manipulator developed at the INSA of Rennes, named PAMINSA, are studied from kinematic, kinetostatic and dynamic points of view. The singular configurations are firstly derived from kinematic aspects. Then, a kinetostatic analysis is performed. For this purpose, the pressure angle is used as a kinetostatic indicator of force transmission. Finally, we present the optimal dynamic conditions generating stable motions inside the singular zones. As a demonstration of the mentioned properties, experimentations are performed on a prototype of PAMINSA.

Fig. 1 .

 1 The PAMINSA manipulator.

  the centre of the platform and O the origin of the base frame (C 1 C 2 C 3 and O 1 O 2 O 3 representing equilateral triangles, P and O are the centre of the circumcircle of these triangles, respectively); in such a case, the platform gains an infinitesimal rotation; -point P of the platform is located on a circle centred in O, of which the radius equal to

2 .

 2 (a) Type 1 singular configuration (b) Type 2 singular configuration (planar equivalent model) Fig. Example of singularities of PAMINSA manipulator.

Fig. 3 .

 3 Fig. 3. The pressure angle of the planar parallel 3-RPR mechanism.

Fig. 4 .

 4 Fig. 4. Trajectory reproduction on the PAMINSA during the displacement of the platform with an arbitrary fifth order polynomial law (view from below).

ON THE KINEMATIC, KINETOSTATIC AND DYNAMIC PROPERTIES OF PARALLEL MANIPULATORS IN THE PRESENCE OF SINGULARITY

SUMMARY

This paper presents the singularity analysis of parallel manipulators from kinematic, kinetostatic and dynamic points of view. Algebraically, a singularity analysis is based on the properties of the Jacobian matrices of the mechanical structure, i.e. when the matrices relating the input and output speeds become rank deficient. However, when parallel manipulators are close to presenting Type 2 singularities, they lose their stiffness and their quality of motion transmission. Therefore, the singularity zones may also be defined via kinetostatic approaches. For this purpose, the pressure angle is used as a kinetostatic indicator of force transmission. However, while it is demonstrated that in Type 2 singularities a parallel manipulator locks up, it has been shown experimentally that, via optimal dynamic control of manipulators, it is possible to pass through these singular zones. Hence, we have determined the optimal dynamic conditions generating stable motions inside the singular zones from the inverse dynamic equations.


Katell Quénéa
email: katell.quenea@sorbonne-universite.fr

Iry Andrianjara

Aleksandar Rankovic

Erika Gan

Emmanuel Aubry

Jean- Christophe Lata

Sébastien Barot

Maryse Castrec-Rouelle

Influence of the residence time of street trees and their soils on trace element contamination in Paris (France)

Keywords: Urban soils, Road traffic impact, Bioaccumulation, Trace element, Leaves, Roots

With the actual increasing interest for urban soils, the evaluation of soil contamination by trace elements and the dynamics of this contamination appear mandatory to preserve plant and thereby human health. Street trees and the associated soil placed in pits located nearby roads could represent convenient indicators of urban and vehicle traffic influences on soils and plants. However, data on these soils remain scarce, many studies investigating park soils rather than street tree soils. Furthermore, trace elements could be one of the main factors causing the 2 observed urban tree decline, while practitioners more and more question the possible reuse of these soils after the death of trees as well as tree litter collected in the streets. We evaluated the contamination in anthropogenic trace elements (TE), namely Zn, Pb and Cd, of street trees (Tilia tomentosa) and their soils distributed allover Paris (France). Street tree soils are imported from rural areas at the plantation of each new tree so that tree age corresponds to the time of residence of the soil within an urban environment allowing the evaluation of temporal trends on TE concentration in soils and trees.

The TE concentration revealed an important soil pollution, especially for the older soils (mean age of 80 years old). The consideration of the residence time of trees and soils in an urban environment evidenced an accumulation of Zn and Pb (ca. 4.5 mg kg -1 yr -1 and 4 mg kg -1 yr -1 for Zn and Pb, respectively). However, leaf concentrations in TE were low and indicate that soil-root transfer was not significant compared to the contamination by atmospheric deposition. These results underlined the necessity to deepen the evaluation of the recycling of urban soils or plants submitted to urban contamination.

Introduction

For decades, trace elements (TE) have been of main concern in environmental survey due to their impact on biodiversity and human health. In urban areas, heavy road traffic, industrial activities and residential heating generate important atmospheric pollution leading to TE deposition [START_REF] Galloway | Trace metals in atmospheric deposition: a review and assessment[END_REF][START_REF] Garnaud | Heavy metal concentrations in dry and wet atmospheric deposits in Paris district: comparison with urban runoff[END_REF][START_REF] Manta | Heavy metals in urban soils: a case study from the city of Palermo (Sicily), Italy[END_REF][START_REF] Basioli | The influence of a large city on some soil properties and metals content[END_REF][START_REF] Wong | Urban environmental geochemistry of trace metals[END_REF][START_REF] Thevenot | Critical budget of metal sources and pathways in the Seine river basin (1994-2003) for Cd, Cr, Cu, Hg, Ni, Pb and Zn[END_REF][START_REF] Schreck | Metal and metalloid foliar uptake by various plant species exposed to atmospheric industrial fallout: Mechanisms involved for lead[END_REF]). In addition, direct inhalation of contaminated atmosphere or street dust enriched in TE by urban inhabitants has deleterious effects on health (Pena-Fernandez et al. 2014). The atmospheric deposition is also source of soil contamination and thereafter of river and groundwater contaminations, through the leaching of impervious urban surfaces.

Finally, TE contamination from the atmosphere to soils and waters induces contamination of plants through atmosphere-plant transfer as well as soil-plant transfer [START_REF] Chojnacka | Bioavailability of heavy metals from polluted soils to plants[END_REF]Kabata Pendias, 2010).

Many studies have focused on TE in urban environments either directly by soil concentration measurements [START_REF] Ge | Trace metal speciation and bioavailability in urban soils[END_REF][START_REF] Manta | Heavy metals in urban soils: a case study from the city of Palermo (Sicily), Italy[END_REF][START_REF] Maher | Spatial variation in vehicle-derived metal pollution identified by magnetic and elemental analysis of roadside tree leaves[END_REF] or through biomonitoring [START_REF] Harmens | Mosses as biomonitors of atmospheric heavy metal deposition: Spatial patterns and temporal trends in Europe[END_REF][START_REF] Deljanin | Chemometrics in biomonitoring: Distribution and correlation of trace elements in tree leaves[END_REF][START_REF] Gillooly | Framework for using deciduous tree leaves as biomonitors for intraurban particulate air pollution in exposure assessment[END_REF]. The use of vegetation as bioindicator of pollution is widely applied, plants being relevant integrator of their environment [START_REF] Markert | Chapter 1 Definitions, strategies and principles for bioindication/biomonitoring of the environment[END_REF]. Thus, measurements of TE concentrations in plants allow the assessment of the overall TE availability to plants without any distinction of the source (atmosphere, soil, water). However, all other things remaining equal (in particular, soil properties) TE concentrations in trees are influenced by tree species [START_REF] Piczak | Metal concentrations in deciduous tree leaves from urban areas in Poland[END_REF][START_REF] Pulford | Phytoremediation of heavy metal-contaminated land by trees-a review[END_REF], the precise localization of the street trees in the city [START_REF] Maher | Spatial variation in vehicle-derived metal pollution identified by magnetic and elemental analysis of roadside tree leaves[END_REF]) and the TE considered and its speciation [START_REF] Kabata-Pendias | Soil-plant transfer of trace elements-an environmental issue[END_REF]. Metals such as lead (Pb) and cadmium (Cd) accumulate close to intense traffic roads and their concentrations decrease exponentially with increasing distance to the road [START_REF] Viard | Integrated assessment of heavy metal (Pb, Zn, Cd) highway pollution: bioaccumulation in soil, Graminaceae and land snails[END_REF][START_REF] Nabulo | Assessment of lead, cadmium, and zinc contamination of roadside soils, surface films, and vegetables in Kampala City, Uganda[END_REF][START_REF] Werkenthin | Metals in European roadside soils and soil solution-A review[END_REF]. Mosses and trees are frequently used in biomonitoring context [START_REF] Markert | The german heavy metal survey by means of mosses[END_REF][START_REF] Piczak | Metal concentrations in deciduous tree leaves from urban areas in Poland[END_REF][START_REF] Baycu | Ecophysiological and seasonal variations in Cd, Pb, Zn, and Ni concentrations in the leaves of urban deciduous trees in Istanbul[END_REF][START_REF] Gratani | Long-term monitoring of metal pollution by urban trees[END_REF], Anicic et al. 2011;[START_REF] Sawidis | Trees as bioindicator of heavy metal pollution in three European cities[END_REF][START_REF] Guéguen | Atmospheric pollution in an urban environment by tree bark biomonitoring-Part I: Trace element analysis[END_REF][START_REF] Natali | Assessment of trace metal air pollution in Paris using slurry-TXRF analysis on cemetery mosses[END_REF]). However, soil-plant transfer has often been neglected. In consequence, the simultaneous analysis of soil and plant present on a same site could help circumscribing limitations occurring when plants or soils are used separately for the evolution of site contamination [START_REF] Mertens | Use and abuse of trace metal concentration in plant tissue for biomonitoring and phytoextraction[END_REF].

The city of Paris (France) is the fifth most important city in Europe in term of population, with a high density (20000 inhabitants per km 2 ). Human activities contribute to a large part of TE in Paris through industry emissions, vehicle exhaust, and residential heating. Despite a large decrease of TE deposition since 1994 (Azimi et al. 2005a), this atmospheric deposition remains the main source of TE, as evidenced by [START_REF] Garnaud | Heavy metal concentrations in dry and wet atmospheric deposits in Paris district: comparison with urban runoff[END_REF] and Azimi et al. (2005a, b). However another source of TE in urban soil is the runoff water from streets and roofs. In Paris, roof runoff was evidenced to be a significant source of Cd, Zn, and Pb [START_REF] Garnaud | Heavy metal concentrations in dry and wet atmospheric deposits in Paris district: comparison with urban runoff[END_REF][START_REF] Gromaire | Impact of zinc roofing on urban runoff pollutant loads: the case of Paris[END_REF][START_REF] Rocher | Hydrocarbons and metals in atmospheric deposition and roof runoff in central Paris[END_REF]) and led to an increase of TE in the Seine river basin [START_REF] Thevenot | Critical budget of metal sources and pathways in the Seine river basin (1994-2003) for Cd, Cr, Cu, Hg, Ni, Pb and Zn[END_REF]. Nonetheless, extensive data on soil contamination by TE close to roads in Paris are still missing. The study of street trees growing in the vicinity of car exhaust and their soil could allow better assessing the extent of TE contamination in Paris. Indeed, atmospheric deposition, or street and roof leaching likely impact soils from those street trees and trees could be contaminated directly by either atmospheric deposition or by soil-plant transfer.

In Paris as in many cities, street trees are planted in pits that have been filed with agricultural soil transported from the country side (Paris Green Space and Environmental Division, pers. comm.). The soil is removed and replaced each time a tree dies and a young one is planted. This procedure provides a unique opportunity to assess the contamination dynamics through the comparison of trees with various ages (until 80 years) and their corresponding soil. Indeed, the age of street trees is also the residence time of the soil within the urban environment [START_REF] Kargar | Trace metal contamination influenced by land use, soil age, and organic matter in Montreal tree pit soil[END_REF]). In addition, while TE accumulate during the whole tree life in their soils, TE accumulate in roots and leaves only during the life span of these organs. Thus, investigating root and leaf TE concentrations might allow distinguishing between the atmospheric or soil sources depending on the intensity of TE translocation between roots and leaves. Indeed, if translocation is low, root TE will mainly come from soil-plant contamination and leaf TE from atmosphere-plant contamination. In addition, leaves record the contamination during a single leafy season whereas roots accumulate TE for several years depending on their size and life span [START_REF] Withington | Comparisons of structure and life span in roots and leaves among temperate trees[END_REF]). In addition, practitioners are so far dumping the soil of dead trees with the belief that these soils are no longer fertile, partially due to contamination by different sources of pollution. The same thing goes for street tree litter collected as it is considered as waste in the EU legislation [START_REF] Nurmatov | High-Quality Solid Fuel Production from Leaf Litter of Urban Street Trees[END_REF]. Consequently, the evaluation of the soil and leaf contamination could help deciding whether street tree soils and leaves should be reused or dumped after tree death and litter collection.

Therefore, our objectives were to evaluate: (i) the TE (Zn, Cd, and Pb) contamination of soils highly exposed to traffic contamination and imported to Paris between 15, 50 and 80 years ago, and (ii) the contamination of roots and leaves from the corresponding street tree (Tilia tomentosa Moench) and thus (iii) the potential soil-plant transfer of these TE. The three model TE were chosen because of their frequently observed anthropogenic origin reported in urban soils as well as their ecological importance: Zn is essential for plant nutrition while Cd and Pb are not, and while Cd and Zn are mobile in soils and available for plants, Pb tend to accumulate mainly in roots and remain at leaf surface (Madejón et al. 2004). The model tree was chosen because it is one of the first dominant species in the streets of Paris.

Materials and methods

Study area and sampling procedure

Thirty roadside linden trees (Tilia tomentosa Moench) were selected as these trees are widespread in Paris (France) (48.8534°N; 2.3488°E). The selected roadside trees were gathered in three age classes: ten trees belonged to the "young" class (between 11 and 17 years old, mean age of 13 years old), ten trees to the "medium" class (between 41 and 67 years old, mean age of 49 years old), and ten trees to the "old" class (69 and 86 years old, mean age of 80 years old). Tree age was determined by dendrochronological methods by [START_REF] David | Street trees in Paris are sensitive to spring and autumn precipitation and recent climate changes[END_REF]. When a new tree is planted, a pit of about 3-4 m 3 is dug and filled with imported soil from surrounding peri-urban agricultural areas. Only vigorous trees with either bare or drain-covered soils were selected to avoid important differences in terms of rooting conditions and water availability [START_REF] Rahman | Effect of rooting conditions on the growth and cooling ability of Pyrus calleryana[END_REF].

Sampling occurred in July 2011 (Fig. 1). Soils were sampled in pits from roadside and roots were isolated from the soil cores. Leaf samples were collected on trees grown in the corresponding pits. Trees were distributed all over Paris, with trees in nearly all Paris districts, to ensure the representativeness of the sampling. Soil samples were collected with an auger in the 10-30 cm horizon depth in pits of the tree selected. For each street tree pit, two cores were sampled and then the composite sample was freeze-dried. Thereafter, samples were sieved (<2 mm) discarding coarse plant residues and roots (around 1mm diameter) were collected. Shadow leaves were cut at minimum 2 m height from all sides of the crown of the trees from which soil samples have been collected.

Sample treatment procedures

Leaves and roots were washed twice with deionized water in ultrasonic bath to remove any particle presents on the surface, and finally dried and grinded.

Pseudo-total metal concentrations were measured after soil mineralization. In a first step, soil samples were mineralized in aqua regia (mixture of 1/3 HNO 3 70% and 2/3 HCl 37%) using a temperature-controlled digestion system (DigiPREP Jr instrument, SCP Science, Baie-d'Urfé, Canada) at 120°C for 8 h and dried.

Leaves and roots were mineralized according to the following procedure: leave and root samples were placed in Teflon flask with HNO 3 70% for 24 h at 120 °C with a DigiPREP instrument. After cooling H 2 O 2 30% was added and Teflon flasks placed at 120 °C for 24 h.

Physico-chemical analyses

Main physico-chemical characteristics of the soil samples are reported in Table 1 and indicate a relative homogeneity in the soil characteristics.

Total organic carbon and nitrogen contents were measured using an elemental analyzer (Carbo Erba instrument CHN NA 1500 series 2, Milan, Italy). Zinc concentrations were measured by inductively coupled plasma-optical emission spectrometry ICP-OES (instrument JY2000), whereas Pb and Cd concentrations were measured by inductively coupled plasma-mass spectrometry ICP-MS (X Series II, Thermo Electron). Ten blank samples were added to the sequence following the same treatment for method control. Each sample was analyzed in triplicate. The detection limits of Pb, Cd, and Zn were 0.3, 0.2, and 2.2 μg L -1 , respectively, whereas the limits of quantification were about 0.4, 0.3, and 3 μg L -1 , respectively. The accuracy of calibrations was checked using a certified reference material (TMDA-64.2) from Environment Canada. The concentrations found corresponded to the certified values +/-5%.

Data treatment and statistical analysis

Data processing and statistical analyses were performed with RStudio 1.0.153 (RStudio Inc., Boston, Massachusetts, USA) using R 3.4.1 (R Foundation for Statistical Computing, Vienna, Austria). Significant differences were determined with the Kruskal-Wallis test (α = 0.05) and Dunn's multiple comparison test (α = 0.05). Plots were achieved with ggplot2.

Results and discussions

Evaluation of trace element contamination of Paris soils sampled in street tree pits

TE concentration measurements in soils revealed a wide range of concentrations depending on the trees age, location, and the TE considered (Fig. 2). Zn and Pb were the most abundant TE with a mean concentration of 229±173 mg•kg -1 and 196±186 mg•kg -1 , respectively. The mean Cd concentration was lower (1.7±0.55 mg•kg -1 ) than Pb and Zn concentrations, as frequently observed due to low Cd natural concentration in the environment [START_REF] Kabata-Pendias | Soil-plant transfer of trace elements-an environmental issue[END_REF]Azimi et al. 2005b). The heterogeneity of TE concentrations reflects the local influence of road traffic density between streets. These concentrations were in line with results from soil samples covering the whole Parisian region with a large range of anthropogenic pressures, but a limited number of samples from Paris city [START_REF] Gaspéri | Contamination of soils by metals and organic micropollutants: case study of the Parisian conurbation[END_REF][START_REF] Foti | Trace element concentrations along a gradient of urban pressure in forest and lawn soils of the Paris region (France)[END_REF]. Nonetheless, the concentrations measured in soils from Paris were in the upper range of concentrations reported in other urban soils (ranging from 36 to 1641 mg.kg -1 , 9 to 252 mg.kg -1 and <0.2 to 2.45 mg.kg -1 for Zn, Pb and Cd, respectively; Table 2) and were included in the upper limit concentration values allowed for sewage sludge application (150-300 mg.kg -1 , 50-300 mg.kg -1 and 1-3 mg.kg -1 for Zn, Pb and Cd, respectively; European Directive 86/278/CEE).

To evaluate soil contamination, we calculated a pollution index (PI) defined as the ratio of the metal concentration to the geochemical background concentration to evaluate the contamination of urban soils compared to rural soils [START_REF] Chen | Assessment of heavy metal pollution in surface soils of urban parks in Beijing, China[END_REF][START_REF] Basioli | The influence of a large city on some soil properties and metals content[END_REF]. According to [START_REF] Basioli | The influence of a large city on some soil properties and metals content[END_REF], PI < 1 reflects a low contamination, 1 < PI < 5, a moderate contamination, and PI > 5, a high contamination. However, in Paris, street tree soils are imported from sites located in the vicinity of Paris (<50 km) and placed in pits before introduction of trees. Thus, we used data from [START_REF] Duigou | Nouvelle collecte nationale d'analyses d'éléments en traces dans les sols (horizons de surface)[END_REF] on mean pedogeochemical background in the region (estimated to 51.0±9.4 mg•kg -1 , 23.1±8.3 mg•kg -1 , and 0.3±0.1 mg•kg -1 , for Zn, Pb, and Cd, respectively) as geochemical background concentration. These values are close to those measured in rural soils from the Parisian region with low anthropogenic influence [START_REF] Saby | Geostatistical assessment of Pb in soil around Paris, France[END_REF][START_REF] Foti | Trace element concentrations along a gradient of urban pressure in forest and lawn soils of the Paris region (France)[END_REF]. Thus, the PI values we respectively calculated for Zn, Pb and Cd, i.e. 4, 8 and 5, indicated an important contamination of soils in Paris.

TE emission related to traffic road, industrial activities, and residential heating was pointed out by many studies as source of TE in atmospheric deposition in cities [START_REF] Manta | Heavy metals in urban soils: a case study from the city of Palermo (Sicily), Italy[END_REF][START_REF] Charlesworth | A comparative study of heavy metal concentration and distribution in deposited street dusts in a large and a small urban area: Birmingham and Coventry, West Midlands, UK[END_REF][START_REF] Basioli | The influence of a large city on some soil properties and metals content[END_REF]). In addition, atmospheric depositions strongly depend on the density of population of the city considered [START_REF] Charlesworth | A comparative study of heavy metal concentration and distribution in deposited street dusts in a large and a small urban area: Birmingham and Coventry, West Midlands, UK[END_REF][START_REF] Davis | Spatial distribution of bulk atmospheric deposition of heavy metals in metropolitan Sydney, Australia[END_REF]. Since the anthropogenic origin of Zn, Pb and Cd has frequently been reported in urban soils [START_REF] Manta | Heavy metals in urban soils: a case study from the city of Palermo (Sicily), Italy[END_REF][START_REF] Rodrigues | The influence of anthropogenic and natural geochemical factors on urban soil quality variability: a comparison between Glasgow, UK and Aveiro, Portugal[END_REF]; Ajmone-Marsan and Biasioli 2010; [START_REF] Gaspéri | Contamination of soils by metals and organic micropollutants: case study of the Parisian conurbation[END_REF]) and since the street tree soils originally come from non-urban areas around Paris, the TE concentrations very likely result from an anthropogenic origin linked to the urban environment such as urban dust samples (de [START_REF] Miguel | Origin and patterns of distribution of trace elements in street dust: Unleaded petrol and urban lead[END_REF][START_REF] Charlesworth | A comparative study of heavy metal concentration and distribution in deposited street dusts in a large and a small urban area: Birmingham and Coventry, West Midlands, UK[END_REF][START_REF] Ayrault | Street dust: source and sink of heavy metals to urban environment[END_REF]). Moreover the high population density in Paris might contribute to explain the important TE contamination we observed.

Many studies compared TE concentrations between soils of different cities and revealed important discrepancies between cities probably due to differences in industrial activities and traffic road intensities [START_REF] Madrid | Variability in concentration of potentially toxic elements in urban parks from six European cities[END_REF][START_REF] Rodrigues | The influence of anthropogenic and natural geochemical factors on urban soil quality variability: a comparison between Glasgow, UK and Aveiro, Portugal[END_REF]; Ajmone-Marsan and Biasioli 2010). Azimi et al. (2005b) have estimated a total TE flux of 103 mg•m -2 •y -1 in Paris downtown, mainly originating from road traffic and residential heating. Zinc was the most abundant anthropogenic metal measured in atmospheric depositions, representing around 50% of the total measured TE (Zn, Pb, Cd and Cu), with constant level throughout the year, followed by Pb and Cu. However, Pb isotope ratio calculated in aerosols from Paris indicated a shift in Pb sources since the 90's from a road traffic origin to an industrial one [START_REF] Widory | The origin of atmospheric particles in Paris: a view through carbon and lead isotopes[END_REF]). This shift was correlated with a decrease of TE deposition (except for Cu and Zn) in the same period (Azimi et al. 2005a). The ban of leaded gasoline in 2000 could have participated to this decrease, as already observed in Great-Britain urban areas [START_REF] Charlesworth | A comparative study of heavy metal concentration and distribution in deposited street dusts in a large and a small urban area: Birmingham and Coventry, West Midlands, UK[END_REF].

The time of residence of soil in Paris, i.e. tree age, significantly influenced soil TE concentrations (Fig. 2). The median concentrations exhibited the same pattern for Zn and Pb, with a statistically significant increase (Dunn test, p<0.05) from soils from young street tree pits to old street tree pits (i.e., for 65 years): from 62 to 365.2 mg•kg -1 for Zn and from 47.36 to 307 mg•kg -1 for Pb, respectively, or six times the initial concentration.

Cd median concentration was close to 1.7 mg•kg -1 , and no significant evolution of concentration with time was evidenced. The increase of Zn and Pb in soils with the duration of the period spent in Paris underlined a TE accumulation around 4.5 mg kg -1 yr -1 and 4 mg kg -1 yr -1 for Zn and Pb, respectively. Although accumulation rates are rarely quantified, our result are consistent with results from other countries on street tree soils (Kagar et al., 2013) and results comparing TE concentrations in park soils from different ages [START_REF] Li | Heavy metal contamination of urban soils and street dusts in Hong Kong[END_REF]Madrid et al. 2002;[START_REF] Chen | Assessment of heavy metal pollution in surface soils of urban parks in Beijing, China[END_REF][START_REF] Peltola | Lead and Cu in contaminated urban soils: Extraction with chemical reagents and bioluminescent bacteria and yeast[END_REF][START_REF] Madrid | Variability in concentration of potentially toxic elements in urban parks from six European cities[END_REF] or urban soils sampled twice with 25 years' time interval [START_REF] Imperato | Spatial distribution of heavy metals in urban soils of Naples city (Italy)[END_REF]. Overall, our results show that was very fruitful to use a soil chronosequence based on street tree age to assess the mean long-term accumulation of TE. Such approach could be applied in all towns where the soil of street trees is imported from outside towns and dumped each time a tree dies.

The PI drastically changed the evaluation of pollution for the different TE according to the age class considered. Indeed, for Zn, young soils reveal a low pollution (PI = 1.2) (contrary to Pb and Cd, Zn being essential to plants, in consequence PI of 1.2 could in consequence not considered to be a pollution), medium soils a moderate pollution (PI = 4.4), and old soils a high pollution (PI = 8.2), whereas Pb pollution is moderate in young soils (PI = 2.05) and high in medium and old soils (PI = 8.4 and 16, respectively), despite Pb banning since 2000. These differences of PI with age classes point to an accumulation of TE in soils mainly through airborne deposition and street leaching (see above). The concentrations in soils from the old class were superior to the thresholds recommended for sewage sludge application. No difference in soil Cd concentrations and PI between age classes was evidenced. However, the PI indicated a high pollution (between 5 and 6.2) for the soils from the three age classes. The high PI even for soil from the young age class suggests a quick accumulation in Cd in soils within the first 15 years of street trees. The absence of Cd concentration increase in soils between younger and older trees together with the fast contamination of the soils of the younger trees remained difficult to explain. A possible explanation would that there is a strong and recent source of Cd pollution. More generally, this points at strong variations in Cd pollution within Paris during the last century.

Trace element contamination of Paris trees

Soil characteristics could influence TE bioavailability to plants (Kabata-Pendias 2004). However, in our study all soils exhibited rather similar characteristics with a pH around 7.5, and a CEC between 11 and 13 cmol kg -1 (Table 1). Thus TE bioavailability was likely equivalent, for example whatever the tree age, for each TE considered. This suggests that differences observed between TE concentrations in tree biomass mainly reflected changes in TE concentrations in soils rather than changes in the proportion of TE that is available. In addition, atmospheric deposition should also contribute to tree contamination.

Trace elements in roots

Median concentrations of the different TE measured in roots were highly contrasted. Zinc was the most abundant TE (186 mg•kg -1 ), followed by Pb (37 mg•kg -1 ) and Cd (1.4 mg•kg -1 ). The high concentration in Zn in roots might be due to the fact that Zn is an essential TE for plants contrary to Pb and Cd [START_REF] Dalcorso | Nutrient metal elements in plants[END_REF]. Lead values in roots were in the range of concentrations measured in linden roots from urban industrial sites in Serbia, where soil Pb concentrations were slightly lower than in soils from Paris [START_REF] Serbula | Assessment of airborne heavy metal pollution using Pinus spp. and Tilia spp[END_REF]. Zinc concentrations in roots and soils from Paris were lower than concentrations in the Serbian sites. The TE concentrations in roots, however, increased with tree age and the time spent in the city. Indeed, concentrations of Zn and Pb in young tree roots were statistically lower than in old tree roots (Fig. 3). Despite low (i.e. below 1) bioconcentration factors (corresponding to the ratio of TE concentrations in roots to TE concentration in soils), TE concentrations in roots were statistically significantly higher in old soils than in young soils (Fig. 3). The increasing TE concentration in roots with tree age is likely due to the progressive accumulation of Pb and Zn in the soil and the transfer from soil to roots during the root life. Similar low bioconcentration factors from soil to roots for Zn and Pb were evidenced by [START_REF] Serbula | Assessment of airborne heavy metal pollution using Pinus spp. and Tilia spp[END_REF] in urban sites. This low bioconcentration reflecting a low Pb transfer from soil to plant could result from i) its low bioavailability, which was often evidenced (Kabata-Pendias, 2004), or ii) the age of the root sampled. Indeed, these root analyzed had a mean diameter <2mm which indicated that their residence time in soil was probably less than three years [START_REF] Withington | Comparisons of structure and life span in roots and leaves among temperate trees[END_REF]

Trace elements in leaves

Tree leaves have been identified as useful biomonitors for TE deposition (reviewed by [START_REF] Gillooly | Framework for using deciduous tree leaves as biomonitors for intraurban particulate air pollution in exposure assessment[END_REF], as TE in the atmosphere can be trapped in the cuticular wax and trichome or even penetrate in stomata [START_REF] Uzu | Foliar lead uptake by lettuce exposed to atmospheric fallout[END_REF][START_REF] Schreck | Metal and metalloid foliar uptake by various plant species exposed to atmospheric industrial fallout: Mechanisms involved for lead[END_REF]. However, in this study, leaf concentrations were measured to evaluate leaf contaminations in TE according to tree age to evaluate a potential root (or soil)-leaf transfer, rather than for biomonitoring. TE median concentrations in leaves were low compared other cities: 0.01, 0.8, and 14.6 mg•kg -1 for Cd, Pb, and Zn, respectively (Fig. 4) and more than ten-times lower than TE concentrations in roots. Similar leaf concentrations were obtained from Tilia spp. leaves sampled in Belgrade by Anicic et al. (2011) and [START_REF] Deljanin | Chemometrics in biomonitoring: Distribution and correlation of trace elements in tree leaves[END_REF], whereas other studies have reported higher TE concentrations in Tilia spp. leaves from European cities and from Istanbul [START_REF] Piczak | Metal concentrations in deciduous tree leaves from urban areas in Poland[END_REF][START_REF] Baycu | Ecophysiological and seasonal variations in Cd, Pb, Zn, and Ni concentrations in the leaves of urban deciduous trees in Istanbul[END_REF][START_REF] Sawidis | Trees as bioindicator of heavy metal pollution in three European cities[END_REF][START_REF] Schreck | Metal and metalloid foliar uptake by various plant species exposed to atmospheric industrial fallout: Mechanisms involved for lead[END_REF]. However a link between those higher leaf concentrations and a potential higher environmental contamination, and transfer, to leaves could not be ascertained since these authors, did not measured TE concentrations in other compartments (soil, root, or the atmosphere). In addition, leaves sampled in our study were washed. This could have lowered the TE leaf concentrations measured as leaf washing removed around 10% of TE (deposited as particulate on leaf surface) [START_REF] Aničic | Trace elements accumulation and temporal trends in leaves of urban deciduous trees (Aesculus hippocastanum and Tilia spp.)[END_REF][START_REF] Deljanin | Chemometrics in biomonitoring: Distribution and correlation of trace elements in tree leaves[END_REF]. In particular, Cd and Zn can penetrate into the leaf but Pb is mostly adsorbed to epicuticular lipids at leaf surfaces (Madejón et al. 2004).

The differences between leaf and root concentrations can be due to four complementary and non-exclusive mechanisms: i) the fact that, for our target species, leaves are shorter-lived than roots and record an annual TE signal whereas roots can grow in soil several years and can accumulate TE more than leaves, ii) a low root-leaf transfer, iii) a low leaf contamination by direct airborne deposition and iv) a low foliar pathway transfer.

When considering soil-plant transfer, the low leaf TE concentrations measured in this study indicated no statistically significant contamination of leaves despite different soil or root TE contamination. This suggests that there was no significant transfer of TE from soils to leaves or from root to leaves. The low or negligible transfer from soil to leaves was already noticed by [START_REF] Chojnacka | Bioavailability of heavy metals from polluted soils to plants[END_REF] and [START_REF] Serbula | Assessment of airborne heavy metal pollution using Pinus spp. and Tilia spp[END_REF] and could be due to the speciation of these TE, with only a low proportion of TE being available for trees. For example, Ajmone-Marsan and Biasioli (2010) indicated that in urban area Pb is adsorbed by Fe and Mn oxides and Pb exhausted by vehicle is mainly present as particulate Pb (PbSO 4 ) with a very small proportion of Pb being soluble and thus bioavailable for trees [START_REF] Smith | Lead contamination of the roadside ecosystem[END_REF][START_REF] Harrison | Chemical associations of lead, Cadmium, Copper, and zinc in street dusts and roadside soils[END_REF].

Thus, the contamination of leaves through airborne deposition appears to be the main likely contamination pathway, explaining the low TE concentration in leaves. In addition, the main source of TE in Paris urban environment reported was the atmospheric deposition [START_REF] Rocher | Hydrocarbons and metals in atmospheric deposition and roof runoff in central Paris[END_REF]Azimi et al. 2005b) and a predominant foliar pathway for metal uptake compared to soil-root pathway for leafy plants (e.g., lettuce, parsley, and ryegrass) and pine was previously reported [START_REF] Hovmand | Root uptake of lead by Norway spruce grown on 210 Pb spiked soils[END_REF][START_REF] Schreck | Metal and metalloid foliar uptake by various plant species exposed to atmospheric industrial fallout: Mechanisms involved for lead[END_REF], suggesting that leaf contamination was mainly driven by airborne deposition. The transfer of Pb and Cd from airborne sources to leaves was also observed by Gajbhiye et al. (2016a) at different sites of an industrial area, and for roadside plants (Gajbhiye et al. 2016b). Moreover, some authors already recognize linden as valuable for biomonitoring urban pollution [START_REF] Sawidis | Trees as bioindicator of heavy metal pollution in three European cities[END_REF][START_REF] Serbula | Assessment of airborne heavy metal pollution using Pinus spp. and Tilia spp[END_REF][START_REF] Deljanin | Chemometrics in biomonitoring: Distribution and correlation of trace elements in tree leaves[END_REF], especially for Pb.

In Paris, TE contamination was inferior to values reported in other European cities such as Venice [START_REF] Rossini | Atmospheric bulk deposition to the lagoon of Venice[END_REF] or Belgrade [START_REF] Mijić | Seasonal variability and source apportionment of metals in the atmospheric deposition in Belgrade[END_REF]): 0.15 and 0.22 mg•m -2 •y -1 for Cd, 3.6 and 21.7 mg•m -2 •y -1 for Pb, and 29 and 41.4 mg•m -2 •y -1 for Zn, respectively. And, according to data from Azimi et al. (2005), the atmospheric deposition fluxes of TE in Paris have been decreasing between 1994 and 2002, reaching 29, 3.6 and 0.15 mg•m -2 •y -1 for Zn, Pb and Cd, respectively, in 2002 as a consequence of the ban of Pb in fuel and an improved treatment of flue gas. In consequence, the transfer of TE from the air to linden leaves might be low. The low concentration in leaves could also indicate that the foliar pathway transfer for linden in this study was not significant, despite a slight enrichment in Pb compared with linden leaves from a less urbanized area (data not shown).

Finally, the atmospheric contamination of linden leaves in Paris could be compared with Belgrade city situation, as atmospheric fluxes and TE leaf concentration are available [START_REF] Mijić | Seasonal variability and source apportionment of metals in the atmospheric deposition in Belgrade[END_REF][START_REF] Deljanin | Chemometrics in biomonitoring: Distribution and correlation of trace elements in tree leaves[END_REF]. TE concentrations in linden leaves were in the same range between Paris and Belgrade, except for Pb, whose concentrations were two times higher in Paris (Table 3). In Paris, Pb deposition fluxes were 6 times lower than in Belgrade [START_REF] Motelay-Massei | Atmospheric bulk deposition of trace metals to the Seine river Basin, France: concentrations, sources and evolution from 1988 to 2001 in Paris[END_REF]. However, in Belgrade, leaded gasoline was still widely used, which could explain the higher Pb fluxes in this city. The lower Pb concentrations in leaves from Belgrade than in leaves from Paris could result from the localization of trees: in Paris, trees were in the vicinity of streets whereas, in Belgrade, sampled trees were in a botanical garden, i.e. further from any street. Another factor might be influential: the sampled linden trees may not belong to the same subspecies or even species in the two towns studied, as the studies in Belgrade include a mix between Tilia tomentosa L. and Tilia cordata Mill. Both are Tilia spp. (e.g. [START_REF] Aničic | Trace elements accumulation and temporal trends in leaves of urban deciduous trees (Aesculus hippocastanum and Tilia spp.)[END_REF]. This comparison reflected the importance of providing details on species and localization of trees in the different sites or cities, as it likely strongly influences the results and their interpretation. Especially, considering street or park trees, or considering trees of different ages for biomonitoring can potentially lead to distinct results in terms of contamination. In consequence, this also illustrates the difficulty of the application of biomonitoring to compare different sites. TE pollution biomonitoring by city plants is frequently applied to evaluate the environmental quality or the impact of industrial activities. However, as noticed by [START_REF] Mertens | Use and abuse of trace metal concentration in plant tissue for biomonitoring and phytoextraction[END_REF], biomonitoring of TE in plants presents some drawbacks and the analysis of soils is also recommended.

In the actual context of increasing interest on urban agriculture, this study underlines the influence of TE accumulation with time for soils exposed to urban environment and thus the necessity to evaluate soil contamination before conversion of urban soil for urban agriculture. Moreover, when soil is imported from outside towns to settle an urban farm, TE likely accumulate in this soil at rates that could be comparable to the rates we assessed in street tree soils, but could depend on the proximity to streets, buildings and industries.

Nonetheless, the speciation and especially the bioavailability of the different TE in soils should be studied in order to understand the fate of TE in urban soils and the possibility of using urban soils for agriculture on the long term without contamination of the produced food. TE deposition on leaves is also of importance in urban context and should be taken into account when the recycling of urban leaf litter is considered.

Conclusions

Our results indicate a pollution of soils for the three TE measured (Zn, Pb, and Cd). In addition, the increasing soil concentrations in Zn and Pb from the young to the old class demonstrate an accumulation of TE with time. This accumulation leads to concentrations higher than the usually recommended threshold values for sewage sludge application, which questions the long term use of urban soils for urban agriculture. Although this increase was not observed for Cd, the PI calculated for this element was consistent with an important pollution whatever the age of the sampled soils. However, tree roots indicated a low bioconcentration factor, despite a slight increase of TE concentration in the old class roots. Thus, Zn, Cd, and Pb available fractions in these urban soils are supposed to be limited, explaining the low soil-plant transfer. As the calculated bioconcentration factors from soil to leaves, and from roots to leaves, indicated no significant transfer, leaf contamination should be mainly indicative of pollution through airborne deposition. 17 508

  CaCO 3 content, pH (H 2 O), cation exchange capacity (CEC; Metson method), and soil texture results were provided by a soil analysis laboratory (INRA, Arras, France) according to standardized French procedures (AFNOR NF ISO 10693, NF ISO 10390, NF X 31-130, NF X 31-107, respectively).

Fig. 1 Fig. 2 :

 12 Fig. 1 Localization of pit soils and trees sampled in Paris city, France (adapted from David et al. 2018). = Young class; = Medium class; = Old class

Fig. 3 :

 3 Fig. 3: Boxplots of Zn, Pb, and Cd concentration in the roots of street trees of the three age classes (centered around 15 years, 50 years and 80 years for young, medium and old class, respectively). Boxplot: horizontal bold lines of the box indicate the median, the lower and upper bounds of the box represent the 25th and 75th percentiles respectively. The vertical doted bars include all values. Different letters indicate significant differences (p<0.05) between the class ages (as determined by a Dunn test).

Fig. 4 :

 4 Fig. 4: Box plots of Zn, Pb, and Cd concentrations (mg kg -1 ) in the leaves of street trees of the three age classes (around 15 years, 50 years and 80 years for young, medium and old class, respectively). Boxplot: horizontal bold lines of the box indicate the median, the lower and upper bounds of the box represent the 25th and 75th percentiles respectively. The vertical doted bars include all values.

Table 1 :

 1 Main soil characteristics of the three age classes of soil pits from Paris (France)

	509
	510
			Organic	Total	Clay (g kg -1 ) Silt (g kg -1 ) Sand (g kg -1 ) CaCO 3 (g	CEC
			carbon	nitrogen				kg -1 )	(cmol
			content (%)	content (%)					kg -1 )
	young class	Median	1.0	0.10	202	553	222	14	13.6
		Standard deviation	0.4	0.03	51	138	163	42	3.2
	medium class	Median	1.7	0.14	165	299	489	49	12.5
		Standard deviation	1.1	0.05	41	89	115	53	3.8
	old class	Median	2.0	0.18	100	115	672	112	11.2
		Standard deviation	1.2	0.08	41	140	153	31	2.8
	511

Table 2 :

 2 Mean trace element (Zn, Pb, Cd) concentrations of some urban soils (mg•kg -1 )

	City	Country	Zn (mg•kg -1 ) Pb (mg•kg -1 ) Cd (mg•kg -1 )	Reference
	Palermo	Italy	138	202	0.68	(Manta et al. 2002)
	Parisian region	France	210.4	102.8	0.4	(Gaspéri et al. 2016)
	urban Parisian region	France	106-174	99-188	0.43-2.45	(Foti et al. 2017)
	Paris	France	229	196	1.7	this study
	Mexico	Mexico	36-1641	9-452		(Morton-Bermea et al. 2009)
	Aveiro	Portugal	46	20		(Madrid et al. 2006)
	Glasgow	Great Britain	199	307		(Madrid et al. 2006)
	Ljubljana	Slovenia	114	78		(Madrid et al. 2006)
	Sevilla	Spain	107	107		(Madrid et al. 2006)
	Torino	Italy	225	144		(Madrid et al. 2006)
	Uppsala	Sweden	112	47		(Madrid et al. 2006)
	Sevilla	Spain	145	137		(Madrid et al. 2006)
	London	Great Britain	108	158	<0.2	(Kelly et al. 1996)
	Hong Kong	China	168	93.4	2.18	(Li et al. 2001)
	Montreal	Canada	262	357	1.08	(Kargar et al. 2013)
	Beijing	China	87.6	66.2		(Chen et al. 2005)
	Torino	Italy	183	149		(Basioli et al., 2006)
	Berlin	Germany	129	76.6	0.35	(Birke and Rauch, 2000)
	Moscow	Russia	104	22.3	0.39	(Ermakov, 2017)

Table 3 :

 3 Comparison of TE concentration and fluxes between Paris (France) and Belgrade (Serbia).

	City	Zn	Pb	Cd	References
	Belgrade 10.00 0.50 0.02	(Deljanin et al. 2016)
	Leaves (mg•kg --1 )
	Paris	14.40 0.90 0.02	This study
	Belgrade 113.0 59.5	0.6	(Mijić et al. 2010)
	Atmospheric fluxes (µg•m -2 •day -1 )
	Paris	82.20 11.50 0.66 (Motelay-Massei et al. 2005)

Acknowledgements

We would like to acknowledge Yannick Agnan for comments on an early version of the manuscript. Sampling campaigns benefited from funding from the Île-de-France region (R2DS), the GIS "Climate, Environment, Society" (CCTV2 Project), the PIR IngEcoTech (IESUM project) and the Sorbonne Universities (Dens' project, Convergences program).