Lorenzo Gagliardini
email: lorenzo.gagliardini@irt-jules-verne.fr

Marc Gouttefarde
email: marc.gouttefarde@lirmm.fr

S Caro

Determination of a Dynamic Feasible Workspace for Cable-Driven Parallel Robots

Keywords: Cable-Driven Parallel Robots, Workspace Analysis, Dynamic Feasible Workspace

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Introduction

Several industries, e.g. the naval and renewable energy industries, are facing the necessity to manufacture novel products of large dimensions and complex shapes. In order to ease the manufacturing of such products, the IRT Jules Verne promoted the investigation of new technologies. In this context, the CAROCA project aims at investigating the performance of Cable Driven Parallel Robots (CDPRs) to manufacture large products in cluttered industrial environments [START_REF] Gagliardini | Discrete reconfiguration planning for cable-driven parallel robots[END_REF][START_REF] Gagliardini | A reconfigurable cable-driven parallel robot for sandblasting and painting of large structures[END_REF]. CDPRs are a particular class of parallel robots whose moving platform is connected to the robot fixed base frame by a number of cables as illustrated in Fig. 1. CDPRs have several advantages such as a high payload-to-weight ratio, a potentially very large workspace, and possibly reconfiguration capabilities.

The equilibrium of the moving platform of a CDPR is classically investigated by analyzing the CDPR workspace. In serial and rigid-link parallel robots, the workspace is commonly defined as the set of end-effector poses where a number of kinematic constraints are satisfied. In CDPRs, the workspace is usually defined as the set of poses where the CDPR satisfies one or more conditions including the static or the dynamic equilibrium of the moving platform, with the additional constraint of non-negative cable tensions. Several workspaces and equilibrium conditions have been studied in the literature.

The first investigations focused on the static equilibrium and the Wrench Closure Workspace (WCW) of the moving platform, e.g. [START_REF] Fattah | Workspace and design analysis of cable-suspended planar parallel robots[END_REF][START_REF] Gouttefarde | Analysis of the wrench-closure workspace of planar parallel cable-driven mechanisms[END_REF][START_REF] Roberts | On the inverse kinematics, statics, and fault tolerance of cable-suspended robots[END_REF][START_REF] Stump | Workspaces of cable-actuated parallel manipulators[END_REF][START_REF] Verhoeven | Advances in Robot Kinematics, chap. Estimating the controllable workspace of tendon-based Stewart platforms[END_REF]. Since cables can only pull on the moving platform, a pose belongs to the WCW if and only if any wrench can be applied by means of non-negative cable tensions. Feasible equilibria of the moving platform can also be analyzed using the Wrench Feasible Workspace (WFW) [START_REF] Bosscher | Wrench-feasible workspace generation for cabledriven robots[END_REF][START_REF] Bouchard | On the ability of a cable-driven robot to generate a prescribed set of wrenches[END_REF][START_REF] Gouttefarde | Interval-analysis-based determination of the wrenchfeasible workspaceof parallel cable-driven robots[END_REF]. By definition, the WFW is the set of wrench feasible platform poses where a pose is wrench feasible when the cables can balance a given set of external moving platform wrenches while maintaining the cable tensions in between given lower and upper bounds. The Static Feasible Workspace (SFW) is a special case of the WFW, where the sole wrench induced by the moving platform weight has to be balanced [START_REF] Pusey | Design and workspace analysis of a 6-6 cablesuspended parallel robot[END_REF]. The lower cable tension bound, τ min , is defined in order to prevent the cables from becoming slack. The upper cable tension bound, τ max , is defined in order to prevent the CDPR from being damaged.

The dynamic equilibrium of the moving platform can be investigated by means of the Dynamic Feasible Workspace (DFW). By definition, the DFW is the set of dynamic feasible moving platform poses. A pose is said to be dynamic feasible if a prescribed set of moving platform accelerations is feasible, with cable tensions lying in between given lower and upper bounds. The concept of dynamic workspace has already been investigated in [START_REF] Barrette | Determination of the dynamic workspace of cable-driven planar parallel mechanisms[END_REF] for planar CDPRs. Barrette et al. solved the dynamic equations of a planar CDPR analytically, providing the possibility to compute the boundary of the DFW. This strategy cannot be directly applied to spatial CDPRs due to the complexity of their dynamic model. In 2014, Kozlov studied in [START_REF] Kozlov | A graphical user interface for the design of cable-driven parallel robots[END_REF] the possibility to investigate the DFW by using a tool developed by Guay et al. for the analysis of the WFW [START_REF] Guay | Measuring how well a structure supports varying external wrenches[END_REF]. However, the dynamic model proposed by Kozlov considers the moving platform as a point mass, neglecting centrifugal and Coriolis forces.

This paper deals with a more general definition of the DFW. With respect to the definitions proposed in [START_REF] Barrette | Determination of the dynamic workspace of cable-driven planar parallel mechanisms[END_REF][START_REF] Kozlov | A graphical user interface for the design of cable-driven parallel robots[END_REF], the DFW considered in the present paper takes into account: (i) The inertia of the moving platform; (ii) The external wrenches applied on the moving platform; (iii) The centrifugal and the Coriolis forces corresponding to a given moving platform twist. The Required Wrench Set (RWS), defined here as the set of wrenches that the cables have to apply on the moving platform in order to satisfy its dynamic equilibrium, is calculated as the sum of these three contributions to the dynamic equilibrium. Then, the corresponding DFW is computed by means of the algorithm presented in [START_REF] Gouttefarde | Advances in Robot Kinematics, chap[END_REF] to analyze the WFW.

Dynamic Model

The CDPR dynamic model considered in this paper consists of the dynamics of the moving platform. A dynamic model taking into account the dynamics of the winches could also be considered but is not used here due to space limitations. Additionally, assuming that the diameters of the cables and the pulleys are small, the dynamics of the pulleys and the cables is neglected.

The dynamic equilibrium of the moving platform is described by the following equation Wτ -

I p p -C ṗ + w e + w g = 0 ( 1
)
where W is the wrench matrix that maps the cable tension vector τ into a platform wrench, and

ṗ = ṫ ω p = ẗ α , (2)
where ṫ = [ṫ x , ṫy , ṫz ] T and ẗ = [ẗ x , ẗy , ẗz ] T are the vectors of the moving platform linear velocity and acceleration, respectively, while ω = [ω x , ω y , ω z ] T and α = [α x , α y , α z ] T are the vectors of the moving platform angular velocity and acceleration, respectively.

The external wrench w e is a 6-dimensional vector expressed in the fixed reference frame F b and takes the form

w e = f T e , m T e T = [ f x , f y , f z , m x , m y , m z ] T (3)
f x , f y and f z are the x, y and z components of the external force vector f e . m x , m y and m z are the x, y and z components of the external moment vector m e , respectively. The components of the external wrench w e are assumed to be bounded as follows

f min ≤ f x , f y , f z ≤ f max (4) m min ≤ m x , m y , m z ≤ m max (5)
According to ( 4) and ( 5), the set [w e ] r , called the Required External Wrench Set (REWS), that the cables have to balance is a hyper-rectangle. The Center of Mass (CoM) of the moving platform, G, may not coincide with the origin of the frame F p attached to the platform. The mass of the platform being denoted by M, the wrench w g due to the gravity acceleration g is defined as follows

w g = MI 3 M Ŝp g ( 6
)
where I 3 is the 3 × 3 identity matrix, MS p = R [Mx p , My p , Mz p ] T is the first momentum of the moving platform defined with respect to frame F b . The vector S p = [x p , y p , z p ] T defines the position of G in frame F p . M Ŝp is the skew-symmetric matrix associated to MS p . The matrix I p represents the spatial inertia of the platform

I p = MI 3 -M Ŝp M Ŝp I p (7)
where I p is the inertia tensor matrix of the moving platform, which can be computed by the Huygens-Steiner theorem from the moving platform inertia tensor, I g , defined with respect to the platform CoM

I p = RI g R T - M Ŝp M Ŝp M (8)
R is the rotation matrix defining the moving platform orientation and C is the matrix of the centrifugal and Coriolis wrenches, defined as

C ṗ = ω ωMS p ωI p ω ( 9
)
where ω is the skew-symmetric matrix associated to ω.

3 Dynamic Feasible Workspace

Standard Dynamic Feasible Workspace

Studies on the DFW have been realised by Barrette et al. in [START_REF] Barrette | Determination of the dynamic workspace of cable-driven planar parallel mechanisms[END_REF]. The boundaries of the DFW have been computed for a generic planar CDPR developing the equations of its dynamic model. Since this method cannot be easily extended to spatial CDPRs, Kozlov proposed to use the method described in [START_REF] Guay | Measuring how well a structure supports varying external wrenches[END_REF] in order to compute the DFW of a fully constrained CDPR [START_REF] Kozlov | A graphical user interface for the design of cable-driven parallel robots[END_REF]. The proposed method takes into account the cable tension limits τ min and τ max in checking the feasibility of the dynamic equilibrium of the moving platform for the following bounded sets of accelerations ẗmin ≤ ẗ ≤ ẗmax (10)

α min ≤ α ≤ α max (11)
where ẗmin , ẗmax , α min , α max are the bounds on the moving platform linear and rotational accelerations. These required platform accelerations define the so-called Required Acceleration Set (RAS), [ p] r . The RAS can be projected into the wrench space by means of matrix I p , defined in [START_REF] Gouttefarde | Geometry selection of a redundantly actuated cable-suspended parallel robot[END_REF]. The set of wrenches [w d ] r generated by this linear mapping is defined as the Required Dynamic Wrench Set (RDWS). No external wrench is applied to the moving platform. Accordingly, the DFW is defined as follows Definition 1. A moving platform pose is said to be dynamic feasible when the moving platform of the CDPR can reach any acceleration included in [ p] r according to cable tension limits expressed by [τ] a . The Dynamic Feasible Workspace is then the set of dynamic feasible poses, [p] DFW .

[

p] DFW = (t, R) ∈ R 3 × SO(3) : ∀ p ∈ [ p] r , ∃τ ∈ [τ] a s.t. Wτ -A p = 0 (12)
In the definition above, the set of Admissible Cable Tensions (ACT) is defined as

[τ] a = {τ | τ min ≤ τ i ≤ τ max , i = 1, . . . , m} (13)

Improved Dynamic Feasible Workspace

The DFW described in the previous section has several limitations. The main drawback is associated to the fact that the proposed DFW takes into account neither the external wrenches applied to the moving platform nor its weight. Furthermore, the model used to verify the dynamic equilibrium of the moving platform neglects the Coriolis and the centrifugal wrenches associated to the CDPR dynamic model.

At a given moving platform pose, the cable tensions should compensate both the contribution associated to the REWS, [w e ] r , and the RDWS, [w d ] r . The components of the REWS are bounded according to (4) and ( 5) while the components of the RDWS are bounded according to [START_REF] Gouttefarde | Advances in Robot Kinematics, chap[END_REF] and [START_REF] Guay | Measuring how well a structure supports varying external wrenches[END_REF].

The dynamic equilibrium of the moving platform is described by [START_REF] Barrette | Determination of the dynamic workspace of cable-driven planar parallel mechanisms[END_REF], where C is related to the Coriolis and centrifugal forces of the moving platform and w g to its weight. These terms depend only on the pose and the twist of the moving platform. For given moving-platform pose and twist, these terms are constant.

Therefore, the DFW definition can be modified as follows.

Definition 2. A moving platform pose is said to be dynamic feasible when, for a given twist ṗ, the CDPR can balance any external wrench w e included in [w e ] r , while the moving platform can assume any acceleration p included in [ p] r . The Dynamic Feasible Workspace is the set of dynamic feasible poses, [p] DFW .

[p] DFW :

∀w e ∈ [w e ] r , ∀ p ∈ [ p] r , ∃τ ∈ [τ] a s.t. Wτ -I p p-C ṗ+w e +w g = 0 (14)
In this definition, we may note that the feasibility conditions are expressed according to three wrench space sets. The first set, [w d ] r , can be computed by projecting the vertices of [ p] r into the wrench space. For a 3-dimensional case study (6 DoF case), [ p] r consists of 64 vertices. The second component, [w e ] r , consists of 64 vertices as well. Considering a constant moving platform twist, the last component of the dynamic equilibrium, w c = {C ṗ + w g }, is a constant wrench. The composition of these sets generates a polytope, [w] r , defined as the Required Wrench Set (RWS).

[w] r can be computed as the convex hull of the Minkowski sum over [w e ] r , [w d ] r and w c , as illustrated in Fig. 2:

[w] r = [w e ] r ⊕ [w d ] r ⊕ w c (15)
Thus, Def. 2 can be rewritten as a function of [w] r .

Definition 3. A moving platform pose is said to be dynamic feasible when the CDPR can balance any wrench w included in [w] r . The Dynamic Feasible Workspace is the set of dynamic feasible poses, [p] DFW .

[p] DFW : ∀w ∈

[w] r , ∃τ ∈ [τ] a s.t. Wτ -I p p + w e + w c = 0 (16)
The mathematical representation in ( 16) is similar to the one describing the WFW. As a matter of fact, from a geometrical point of view, a moving platform pose will be dynamic feasible if

[w] r is fully included in [w] a [w] r ⊆ [w] a (17)
Consequently, the dynamic feasibility of a pose can be verified by means of the hyperplane shifting method [START_REF] Bouchard | On the ability of a cable-driven robot to generate a prescribed set of wrenches[END_REF][START_REF] Gouttefarde | Advances in Robot Kinematics, chap[END_REF][START_REF] Guay | Measuring how well a structure supports varying external wrenches[END_REF]. The distances between the facets of the avail- -100

N ≤ f x , f y , f z ≤ 100 N (19) -1 Nm ≤m x , m y , m z ≤ 1 Nm (20)
Similarly, the range of accelerations of the moving platform is limited according to the following inequalities:

-2 m/s 2 ≤ ẗx , ẗy , ẗz ≤ 2 m/s 2 (21) -0.1 rad/s 2 ≤α x , α y , α z ≤ 0.1 rad/s 2 (22)
For the foregoing conditions, the improved DFW of the CDPR covers the 47.96% of its volume. Figure 4(a) illustrates the improved DFW of the CDPR under study.

The results have been compared with respect to the dynamic feasibility conditions described by Def. 1. By considering only the weight and the inertia of the moving platform, the DFW covers the 63.27% of the volume occupied by the DFW, as shown in Fig. 4(b). Neglecting the effects of the external wrenches and the Coriolis forces, the volume of the DFW is 32% larger than the the volume of the improved DFW.

Similarly, by neglecting the inertia of the CDPR and taking into account only the external wrenches w e , the WFW occupies the 79.25% of the CDPR volume. By taking into account only the weight of the moving platform, the SFW covers 99.32% of the CDPR volume. These results are summarized in Tab. 1.

Conclusion

This paper introduced an improved dynamic feasible workspace for cable-driven parallel robots. This novel workspace takes into account: (i) The inertia of the moving platform; (ii) The external wrenches applied on the moving platform and (iii) The centrifugal and the Coriolis forces induced by a constant moving platform twist. As an illustrative example, the static, wrench-feasible, dynamic and improved dynamic workspaces of a spatial suspended cable-driven parallel robot, with the dimensions of a prototype developed in the framework of the IRT JV CAROCA project, are traced. It turns out that the IDFW of the CDPR under study is respectively 1.32 times, 1.65 times and 2.07 times smaller than its DFW, WFW and SFW.

Fig. 1

 1 Fig. 1 Example of a CDPR design created in the framework of the IRT JV CAROCA project.

Fig. 2

 2 Fig. 2 Computation of the RWS [w] r . Example of a planar CDPR with 3 actuators and 2 translational DoF.

Fig. 3

 3 Fig.3Layout of the CoGiRo cable-suspended parallel robot[START_REF] Gouttefarde | Geometry selection of a redundantly actuated cable-suspended parallel robot[END_REF] with the size of the IRT JV CAROCA prototype.

Fig. 4

 4 Fig. 4 (a) Improved DFW and (b) DFW of the CDPR under study covering 47.96% and 63.27% of its volume, respectively.

Table 1

 1 Comparison of SFW , W FW , DFW and IDFW of the CDPR under study. Covered Volume of the CDPR 99.32% 79.25% 63.27% 47.95%

	Workspace type	SFW	W FW	DFW	IDFW

Acknowledgements

This research work is part of the CAROCA project managed by IRT Jules Verne (French Institute in Research and Technology in Advanced Manufacturing Technologies for Composite, Metallic and Hybrid Structures). The authors wish to associate the industrial and academic partners of this project, namely, STX, DCNS, AIRBUS and CNRS.


Éric Lichtfouse

Sylvie Derenne

André Mariotti

Claude Largeau

Possible algal origin of long chain odd n-alkanes in immature sediments as revealed by distributions and carbon isotope ratios

Keywords: carbon-13, n-alkane, n-alkene, Pula oil shale, Botryococcus braunii, alga, plant, waxes, sediment

A Pliocene oil shale (Pula, Hungary), a C 3 plant Triticum aestivum and a C 4 plant Zea mays were compared using isotopic composition of bulk organic matter, along with distributions and individual carbon isotope ratios of n-alkanes from organic extracts. The microalga Botryococcus braunii (A race) was thus shown to be the main source of the predominant 27, 29 and 31 n-alkanes of Pula sediment. Therefore, the dominance of odd carbon-numbered n-alkanes in the range C 25 to C 35 in extracts from immature sediments shall not be systematically assigned to higher plant contribution but algal input has also to be tested via molecular isotope ratios. In fact, the long chain n-alkanes with an odd predominance observed in extracts of various immature sediments are likely to be derived, at least partially, from algae.

INTRODUCTION

n-Alkanes occur almost ubiquitously in soils, sediments, petroleums and coals [START_REF] Eglinton | Organic Geochemistry. The Organic Chemist's Approach[END_REF][START_REF] Morrisson | Soil Lipids. In Organic Geochemistry, Methods and Results[END_REF][START_REF] Albrecht | Biogenic substances in sediments and fossils[END_REF][START_REF] Tissot | Petroleum Formation and Occurrence[END_REF] and their distribution has been widely used for source organism identification and as a maturation parameter. Markedly different pathways can be implicated, however, in n-alkane formation. Indeed, such compounds are likely to represent a direct contribution of natural waxes in some immature sediments, whereas they appear to be mainly formed by thermal breakdown of kerogen in mature sediments and petroleums. In this connection, kerogen fractions derived from the selective preservation of resistant, highly aliphatic, biomacromolecules have been recently shown to be especially prolific materials for the catagenic production of n-alkanes (Largeau et al., 1986;[START_REF] Tegelaar | Possible origin of n-alkanes in high-wax crude oils[END_REF][START_REF] Leeuw | A review of macromolecular organic compounds that comprise living organisms and their role in kerogen, coal and petroleum formation[END_REF]. n-Alkanes can also arise by degradation of biological aliphatic precursors such as n-alcohols and n-carboxylic acids [START_REF] Tissot | Petroleum Formation and Occurrence[END_REF][START_REF] Lichtfouse | Tracing biogenic links of natural organic substances at the molecular level with stable carbon isotopes: n-alkanes and n-alkanoic acids from sediments[END_REF]and refs. therein).

n-Alkanes exhibiting a pronounced odd carbon-number predominance in the range C 25 to C 35 have often been used to indicate a terrestrial contribution in sediments because similar distributions are observed in leaf waxes of higher plants. However, n-alkenes also showing an odd predominance in the same range occur in various microalgae (Kolattukudy, 1976). Through diagenetic reduction, these algal constituents might thus represent an important source of sedimentary n-alkanes. Isotopic analysis at the molecular level is actually the sole method which could allow to discriminate between these two origins and thus provide direct information on contributing organisms. In the present study, this method was applied to the hydrocarbons isolated from the extract of an important, organic-rich, Pliocene deposit from Pula (Hungary). The bulk carbon isotope ratio of this oil shale was also determined. Parallel measurements were carried out, for comparative purposes, on Triticum aestivum, a C 3 plant, and Zea mays, a C 4 plant. The major aim of these isotopic studies was to specify the origin of the n-alkanes occurring in Pula extract, to derive information on the relative contributions of terrestrial and algal inputs to this sediment and, in a more general way, to test the suitability of odd, long chain, n-alkanes as markers of higher plant contribution.

EXPERIMENTAL

Detailed procedures are described elsewhere [START_REF] Metzger | An n-alkatriene and some n-alkadienes from the A Race of the green alga Botryococcus braunii[END_REF][START_REF] Lichtfouse | A molecular and isotopic study of the organic matter from the Paris Basin, France[END_REF]. Leaves from two plants of different mode of CO 2 fixation, T. aestivum and Z. mays, were collected in 1992 in an experimental field at Boigneville, France. The tested Pula sample contained about 45% of TOC; this oil shale, comprising immature type I kerogen, is a typical maar lake deposit [START_REF] Brukner-Wein | Organic Geochemistry of alginite deposited in a volcanic crater lake[END_REF]. n-Alkanes were isolated from Pula sediment extract and leaf extracts, then purified by successive column and thin layer chromatography. They were identified by gas chromatography-mass spectrometry and co-elution with standards. Bulk isotopic compositions were measured on a Carlo Erba NA 1500 elemental N and C analyser coupled to a VG Sira 10 mass spectrometer. Such measurements were carried out on Z. mays and T. aestivum leaves, on HCl-decarbonated Pula oil shale and on the kerogen isolated from this shale by a classical HCl-HF treatment. Isotopic analyses of individual n-alkanes were carried out under a continuous helium flow using an HP 5890 gas chromatograph coupled with a CuO furnace (850°C) and a cryogenic trap (-100°C) coupled with a VG Optima mass spectrometer, monitoring continuously ion currents at m/z = 44, 45 and 46. Carbon isotopic compositions are expressed in per mil. relative to the Pee Dee Belemnite standard: δ 13 C = [( 13 C/ 12 C sample -13 C/ 12 C std)/( 13 C/ 12 C std)] x 10 3 , where 13 C/ 12 C std = 0.0112372. Significant measurements of isotope ratios cannot be achieved when some overlapping of GC peaks occurs [START_REF] Lichtfouse | Enhanced resolution of organic compounds from sediments by isotopic gas chromatography-combustion-mass spectrometry[END_REF]. Accordingly, the isotopic composition of n-heptacosane from Pula sediment is not reported due to the presence of a nearly co-eluting C 27 monounsaturated hydrocarbon.

RESULTS AND DISCUSSION

Isotopic composition of bulk organic matter

Common higher plants can be classified into two isotopic categories according to their mode of CO 2 fixation [START_REF] Smith | Two categories of 13 C/ 12 C ratios for higher plants[END_REF]Epstein, 1971, O'Leary, 1981) To evaluate the contribution of terrestrial plants in Pula sediment, the bulk isotopic compositions of this oil shale, of a modern C 3 plant (wheat) and a modern C 4 plant (maize) were compared. However, such a comparison must take into account the difference of isotopic composition of atmospheric CO 2 between Pliocene and present. The present isotopic composition of CO 2 is 7.8‰ while the pre-industrial value was about 1-1.5‰ heavier and did not undergo significant changes during geological times, except sharp variations at era boundaries [START_REF] Shackleton | The carbon isotope record of the Cenozoic: history of organic carbon burial and of oxygen in the ocean and atmosphere[END_REF][START_REF] Schlanger | The Cenomanian-Turonian Oceanic Anoxic Event, I. Stratigraphy and distribution of organic carbon-rich beds and the marine δ 13 C excursion[END_REF][START_REF] Marino | Isotopic composition of atmospheric CO 2 inferred from carbon in C4 plant cellulose[END_REF][START_REF] Raymo | Response of deep ocean circulation to initiation of northern hemisphere glaciation (3-2 MA)[END_REF]. Accordingly, a corrective term of +1.5‰ was applied to modern isotopic values in order to allow for a significant comparison with Pula sediment (Table 1). Pula sediment -19.03* -28.7 -30.7 -28.1 -30.9 -28.8 -30.0 -28.8 ___________________________________________________________________________________________ * It is well documented that B. braunii fossilization takes place via the selective preservation of the non-hydrolysable aliphatic biopolymer building up the outer walls. In the living algae, this material is formed by polymerization of high molecular weight lipids comprising long alkyl chains. In the A race, the biosynthetic pathways implicated in the production of the resistant biopolymer and of n-alkadienes are related. Accordingly, relatively close isotopic ratios are expected for the above compounds. The large difference noted between the bulk isotope ratio of the HCl-decarbonated sediment, on one hand, and the n-alkanes of sediment extract, on the other hand, shall reflect the somewhat heterogenous nature of the sediment. Indeed, even in Torbanites, which are sedimentary rocks chiefly composed of fossil Botryococcus accumulation, micro-FTIR observations revealed the presence of an interstitial organo-mineral matrix which organic constituents are sharply different from those of Botryococcus colonies [START_REF] Landais | Chemical caracterization of torbanites by transmission micro-FTIR spectroscopy: origin and extent of compositional heterogeneities[END_REF]. In fact, further treatment of the decarbonated Pula sediment with HF-HCl results in a marked shift of the bulk isotope ratio to a lighter value: the kerogen isolated after elimination of the chemically labile constituents exhibits a bulk isotope ratio of -23.68‰. The difference still observed between this value and the average isotope ratios of the extracted n-alkanes should mainly reflect the occurrence, along with the predominant Botryococcus colonies observed by SEM, of non-hydrolysable materials derived from other sources.

The pronounced isotopic differences between the sediment and the two plants indicate that a large input of terrestrial material is unlikely (Table 1). Furthermore, the isotopic value of the Pliocene sediment (-19.03 ‰) falls into the corrected isotopic range of algae (-21.5‰ to -10.5‰). The major algal contribution thus suggested is consistent with the abundant presence of fossil remains of the colonial microalga Botryococcus braunii observed by scanning electron microscopy in Pula oil shale [START_REF] Solti | Prospection and utilization of alginite and oil shale in Hungary[END_REF].

n-Alkane distributions and isotopic compositions

The n-alkanes isolated from the extract of Pula sediment range from C 16 to C 37 with a strong predominance of C 27 , C 29 and C 31 homologues (Figure 1). A similar predominance is typically observed in higher plant waxes (Kolattukudy, 1976), as illustrated in Figure 1 in the case of wheat and maize leaves. It shall be noted, however, that one of the three races known to occur in B. braunii [START_REF] Metzger | Lipids and macromolecular lipids of the hydrocarbonrich microalga Botryococcus braunii. Chemical structure and biosynthesis -Geochemical and Biotechnological importance[END_REF] is characterized by an abundant production of odd carbon-numbered n-alkadienes with a very strong predominance of the C 27 , C 29 and C 31 homologues (Fig. 1). These dienes were identified as the heptacosa-1,18 Z-diene, the nonacosa-1,20 Z-diene and the hentriaconta-1,22 Z-diene, respectively [START_REF] Knights | Hydrocarbons from the green form of the freshwater alga Botryococcus braunii[END_REF][START_REF] Metzger | An n-alkatriene and some n-alkadienes from the A Race of the green alga Botryococcus braunii[END_REF]. Based on their distribution, the n-alkanes of Pula sediment extract could be therefore derived from higher plant waxes or from the reduction of B. braunii n-alkadienes. It shall be noted, however, that the relative abundance of C 27 , C 29 and C 31 n-alkanes from the sediment are close to the relative abundance of B. braunii n-alkadienes. Moreover, both distributions maximize at C 27 instead of C 29 for maize and wheat. The corrected isotopic compositions observed for the C 27 , C 29 , C 31 and C 33 n-alkanes from maize, averaging at -18.6‰, and wheat, averaging at -35.0‰ (Table 1 and Fig. 2) are similar to those previously observed for n-alkanes from various C 4 and C 3 higher plants, respectively [START_REF] Rieley | Sources of sedimentary lipids deduced from stable carbon-isotope analyses of individual compounds[END_REF][START_REF] Rieley | Gas chromatography/Isotope Ratio Mass Spectrometry of leaf wax n-alkanes from plants of differing carbon dioxide metabolisms[END_REF]. Markedly different ratios, averaging at -30.5‰, are obtained for the odd-carbon numbered n-alkanes of Pula sediment extract. Accordingly, based on these isotope ratios, the predominant occurrence of C 27 , C 29 and C 31 n-alkanes in Pula extract is unlikely to reflect a large input of terrestrial plant waxes. On the contrary, based both on their isotopic composition and distribution, such n-alkanes should indicate a major contribution of the alkadiene-producing race of B. braunii (A race). It can be noted that n-alkanes in the range C 25 to C 35 exhibiting an odd predominance and an isotopic composition in the range -30 to -27‰ have been shown to occur in extracts of various low maturity sediments [START_REF] Rieley | Sources of sedimentary lipids deduced from stable carbon-isotope analyses of individual compounds[END_REF][START_REF] Collister | An isotopic biogeochemical study of the Green River oil shale[END_REF][START_REF] Lichtfouse | Tracing biogenic links of natural organic substances at the molecular level with stable carbon isotopes: n-alkanes and n-alkanoic acids from sediments[END_REF][START_REF] Lichtfouse | A molecular and isotopic study of the organic matter from the Paris Basin, France[END_REF][START_REF] Collister | Partial resolution of sources of nalkanes in the saline portion of the Parachute Creek Member, Green River Formation (Piceance Creek Basin, Colorado)[END_REF]. Based on their isotope ratios and distributions, these n-alkanes should not be chiefly derived from terrestrial waxes but more likely from algal lipids.

CONCLUSION

A strong predominance of odd carbon-numbered n-alkanes in the range C 25 to C 35 in sediment extracts shall not be systematically assigned to a contribution of terrestrial plant waxes. In fact, as shown here in the case of Pula oil shale via isotopic and molecular studies, such a feature can be also associated with a major input of microalgae. In addition, the occurrence of long chain, odd n-alkanes, with isotope ratios from -30‰ to -27‰, previously observed in extracts of various immature sediments is likely to reflect an important algal contribution.

  . C 3 plants incorporate CO 2 from the atmosphere by ribulose bisphosphate carboxylation (Calvin cycle) and show isotopic values ranging from -34‰ to -24‰. C 4 plants fix CO 2 by phosphoenol pyruvate carboxylation (Hatch-Slack cycle) and show isotopic values ranging from -19‰ to -6‰. Algae have intermediate values of -23‰ to -12‰.

Fig. 1 .

 1 Fig. 1. Distribution of linear hydrocarbons in wheat and maize leaf waxes, extant B. braunii (A race) and Pula sediment extract. Relative concentrations were calculated by normalization of area obtained by gas chromatography using a flame ionization detector.

Fig. 2 .

 2 Fig. 2. Carbon isotope composition of n-alkanes from maize and wheat leaf waxes and Pula sediment extract. Plant values are corrected to take into account the isotopic difference between ancient and modern atmospheric CO 2 (+1.5‰).

Table 1 .

 1 Carbon isotope composition of bulk organic matter and n-alkanes from maize leaves, a C 4 plant, wheat leaves, a C 3 plant, and Pula sediment. Values in parentheses take into account the isotopic difference between ancient and modern atmospheric CO 2 (+1.5‰).

	___________________________________________________________________________________________
		Bulk organic			n-alkanes (carbon number)
		matter	27	28	29	30	31	32	33	34
	Zea Mays (maize)	-13.18	-19.1		-18.4		-20.6		-22.2
		(-11.68)	(-17.6)		(-16.9)		(-19.1)		(-20.7)
	Triticum aestivum (wheat)	-29.61	-35.9		-36.5		-36.7		-36.7
		(-28.11)	(-34.4)		(-35.0)		(-35.2)		(-35.2)

Acknowledgements-Drs. M. Hetényi and A. Brukner-Wein are gratefully acknowledged for providing a sample of Pula oil shale and general information on this material. We thank Dr. Hervé Bocherens for helpful discussions. We are indebted to G. Bardoux, M. Grably and C. Girardin for MS assistance. An anonymous reviewer is also acknowledged for helpful comments.


Angelos Platis

Tahir Rasheed

Philippe Cardou

Stéphane Caro

Isotropic Design of the Spherical Wrist of a Cable-Driven Parallel Robot

Keywords: Parallel mechanism, cable-driven parallel robot, parallel spherical wrist, wrenches, dexterity

Because of their mechanical properties, parallel mechanisms are most appropriate for large payload to weight ratio or high-speed tasks. Cable driven parallel robots (CDPRs) are designed to offer a large translation workspace, and can retain the other advantages of parallel mechanisms. One of the main drawbacks of CD-PRs is their inability to reach wide ranges of end-effector orientations. In order to overcome this problem, we introduce a parallel spherical wrist (PSW) end-effector actuated by cable-driven omni-wheels. In this paper we mainly focus on the description of the proposed design and on the appropriate placement of the omni-wheels on the wrist to maximize the robot dexterity.

Introduction

Several applications could benefit from CDPRs endowed with large orientation workspaces, such as entertainment and manipulation and storage of large and heavy parts. This component of the workspace is relatively small in existing CDPR designs.To resolve this problem, a parallel spherical wrist (PSW) end-effector is introduced and connected in series with the translational 3-DOF CDPR to provide an unbounded singularity-free orientation workspace.

IRCCyN, École Centrale de Nantes, 1 rue de la Noë, 44321, Nantes, France, e-mail: {Angelos.Platis, Tahir.Rasheed}@eleves.ec-nantes.fr Laboratoire de robotique, Département de génie mécanique, Université Laval, Quebec City, QC, Canada. e-mail: pcardou@gmc.ulaval.ca CNRS-IRCCyN, 1 rue de la Noë, 44321, Nantes, France, e-mail: stephane.caro@irccyn.ecnantes.fr 1 This paper focuses on the kinematic design and analyis of a PSW actuated by the cables of a CDPR providing the robot independent translation and orientation workspaces. CDPRs are generally capable of providing a large 3-dofs translation workspace, normally needed four cables, which enable the user to control the point where all of them are concentrated [START_REF] Bahrami | Optimal design of a spatial four cable driven parallel manipulator[END_REF], [START_REF] Hadian | Kinematic isotropic configuration of spatial cable-driven parallel robots[END_REF].

Robots that can provide large orientation workspace have been developed using spherical wrist in the past few years that allows the end-effector to rotate with unlimited rolling, in addition to a limited pitch and yaw movements [START_REF] Bai | Modelling of a spherical robotic wrist with euler parameters[END_REF], [START_REF] Wu | Dynamic modeling and design optimization of a 3-dof spherical parallel manipulator[END_REF]. Eclipse II [START_REF] Kim | Eclipse-ii: a new parallel mechanism enabling continuous 360-degree spinning plus three-axis translational motions[END_REF] is an interesting robot that can provide unbounded 3-dofs translational motions, however its orientation workspace is constrained by structural interference and rotation limits of the spherical joints.

Several robots have been developed in the past having decoupled translation and rotational motions. One interesting concept of such a robot is that of the Atlas Motion Platform [START_REF] Hayes | Atlas motion platform: Full-scale prototype[END_REF] developed for simulation applications. Another robot with translation motions decoupled from orientation motions can be found in [START_REF] Yime | A novel 6-dof parallel robot with decoupled translation and rotation[END_REF]. The decoupled kinematics are obtained using a triple spherical joint in conjunction with a 3-UPS parallel robot.

In order to design a CDPR with a large orientation workspace, we introduce a parallel spherical wrist (PSW) end-effector actuated by cable-driven omni-wheels. In this paper we mainly focus on the description of the proposed design and on the appropriate placement of the omni-wheels on the wrist to maximize the robot dexterity.

Manipulator Architecture

The end-effector is a sphere supported by actuated omni-wheels as shown in Fig. 1. The wrist contians three passive ball joints at the bottom and three active omniwheels being driven through drums. Each cable makes several loops around each drum. Both ends are connected to two servo-actuated winches, which are fixed to the base. When two servo-actuated winches connected to the same cable turn in the same direction, the cable circulates and drives the drum and its associated omniwheel. When both servo-actuated winches turn in opposite directions, the length of the cable loop changes, and the sphere centre moves. To increase the translation workspace of the CDPR, another cable is attached, which has no participation in the omni-wheels rotation. The overall design of the manipulator is shown in Fig. 2.

We have in total three frames. First, the CDPR base frame (F 0 ), which is described by its center O 0 having coordinates x 0 , y 0 , z 0 . Second, the PSW base frame (F 1 ), which has its center O 1 at the geometric center of the sphere and has coordinates x 1 , y 1 , z 1 . Third, the spherical end-effector frame (F 2 ) is attached to the end-effector. Its centre O 2 coincides with that of the PSW base frame (O 2 ≡ O 1 ) and its coordinates are x 2 , y 2 , z 2 .

Exit points A i are the cable attachment points that link the cables to the base. All exit points are fixed and expressed in the CDPR reference frame F 0 . Anchor points B i are the platform attachment points. These points are not fixed as they depend to winch #1 to winch #2 actuated omni-wheel passive ball joint drum to winch #7 Fig. 1: Isotropic design of the parallel spherical wrist on the vector P, which is the vector that contains the pose of the moving platform expressed in the CDPR reference frame F 0 . The remaining part of the paper aims at finding the appropriate placement of the omni-wheels on the wrist to maximise the robot dexterity.

Kinematic Analysis of the Parallel Spherical Wrist

Parameterization

To simplify the parameterization of the parallel spherical wrist, some assumptions are made. First, all the omni-wheels are supposed to be normal the sphere. Second, the contact points of the omni-wheels with the sphere lie in the base of an inverted cone where its end is the geometrical center of the sphere parametrized by angle α.

x 0 y 0 z 0 O 0 F 0 x 1 y 1 z 1 z 2 x 2 y 2 O 1,2 F 1 F 2 A 1 A 2 A 3 A 4 B 1 B 2 B 3 B 4 1 2 3 4 5 6 7
Fig. 2: Concept idea of the manipulator Third, the three contact points form an equilateral triangle as shown in [START_REF] Hayes | Atlas motion platform: Full-scale prototype[END_REF][START_REF] Hayes | Atlas motion platform generalized kinematic model[END_REF]. Fourth, the angle between the tangent to the sphere and the actuation force produced by the ith actuated omni-wheel is named β i , i = 1, 2, 3, and β 1 = β 2 = β 3 = β . Figure 3 illustrates the sphere, one actuated omni-wheel and the main design variables of the parallel spherical wrist. Π i is the plane tangent to the sphere and passing through the contact point G i between the actuated omni-wheel and the sphere. ω i denotes the angular velocity vector of the ith actuated omni-wheel. s i is a unit vector along the tangent line T that is tangent to the base of the cone and coplanar to plane Π i . w i is a unit vector normal to s i . f ai depicts the transmission force lying in plane Π i due to the actuated omni-wheel. α is the angle defining the altitude of contact points G i (α ∈ [0, π]). β is the angle between the unit vectors s and

v i (β ∈ [-Π 2 , Π 2
]). As the contact points G i are the corners of an equilateral triangle, the angle between the contact point G 1 and the contact points G 2 and G 3 is equal to γ. R is the radius of the sphere. r i is radius of the i th actuated omni-wheel. φi is the angular velocity of the omni-wheel. u i , v i , n i are unit vectors at point G i and i, j, k are unit vectors along x 2 , y 2 , z 2 respectively.

In order to analyze the kinematic performance of the parallel spherical wrist, an equivalent parallel robot (Fig. 4) having six virtual legs is presented, each leg having a spherical, a prismatic and another spherical joints connected in series. Three legs have an actuated prismatic joint (green), whereas the other three legs have a locked prismatic joints (red). Here, the kinematics of the spherical wrist is analyzed with screw theory and an equivalent parallel robot represented in Fig. 4.

Kinematic Modeling

Fig. 4(a) represents the three actuation forces f ai , i = 1, 2, 3 and the three constraint forces f ci , i = 1, 2, 3 exerted by the actuated omni-wheels on the sphere. The three constraint forces intersect at the geometric center of the sphere and prevent the latter from translating. The three actuation forces generated by the three actuated omniwheels allow us to control the three-dof rotational motions of the sphere. Fig. 4(b) depicts a virtual leg corresponding to the effect of the ith actuated omni-wheel on the sphere. The kinematic model of the PSW is obtained by using the theory of reciprocal screws [START_REF] Ball | A treatise on the theory of screws[END_REF][START_REF] Hunt | Kinematic geometry of mechanisms[END_REF] as follows:

A t = B φ ( 1
)
where t is the sphere twist, φ = φ1 φ2 φ3 T is the actuated omni-wheel angular velocity vector. A and B are respectively the forward and inverse kinematic Jacobian matrices of the PSW and take the form:

A = A rω A rp 0 3×3 I 3 (2)
B = I 3 0 3×3 (3) 0 G 2 G 3 G 1 B 2 B 3 B 1 A 2 A 3 A 1 Locked Prismatic Joint Actuated Prismatic Joint f a1 f a2 f a3 f c1 f c2 f c3 G
A rω =   R(n 1 × v 1 ) T R(n 2 × v 2 ) T R(n 3 × v 3 ) T   and A rp =   v T 1 v T 2 v T 3   (4)
As the contact points on the sphere form an equilateral triangle, γ = 2π/3. As a consequence, matrices A rω and A rp are expressed as functions of the design parameters α and β :

A rω = R 2    -2CαCβ -2Sβ 2SαCβ
CαCβ + √ 3Sβ Sβ - √ 3CαCβ 2SαCβ
CαCβ - √ 3Sβ Sβ + √ 3CαCβ 2SαCβ    (5)
A rp = 1 2    -2CαSβ 2Cβ 2SαSβ CαSβ - √ 3Cβ -( √ 3CαSβ +Cβ ) 2SαSβ CαSβ + √ 3Cβ √ 3CαSβ -Cβ 2SαSβ    (6)
where C and S denote the cosine and sine functions, respectively.

Singularity Analysis

As matrix B cannot be rank deficient, the parallel spherical wrist meets singularities if and only if (iff) matrix A is singular. From Eqs. ( 5) and ( 6), matrix A is singular

Ι 0 G 2 G 3 G 1 f a1 f a2 f a3 (a) β = ±π/2 0 G 2 G 3 G 1 f a1 f a2 f a3 (b) α = π/2 and β = 0
det(A) = 3 √ 3 2 R 3 SαCβ (1 -S 2 αC 2 β ) = 0 (7)
namely, if α = 0 or π; if β = ±π/2; if α = π/2 and β = 0 or ±π.

Figs. 5a and 5b represent two singular configurations of the parallel spherical wrist under study. The three actuation forces f a1 , f a2 and f a3 intersect at point I in Fig. 5a. The PSW reaches a parallel singularity and gains an infinitesimal rotation (uncontrolled motion) about an axis passing through points O and I in such a configuration. The three actuation forces f a1 , f a2 and f a3 are coplanar with plane (X 1 OY 1 ) in Fig. 5b. The PSW reaches a parallel singularity and gains two-dof infinitesimal rotations (uncontrolled motions) about an axes that are coplanar with plane (X 1 OY 1 ) in such a configuration.

Kinematically Isotropic Wheel Configurations

This section aims at finding a good placement of the actuated omni-wheels on the sphere with regard to the manipulator dexterity. The latter is evaluated by the condition number of reduced Jacobian matrix J ω = rA -1 rω which maps angular velocities of the omni-wheels φ to the required angular velocity of the end-effector ω. From Eqs. ( 5) and ( 6), the condition number κ F (α, β ) of J ω based on the Frobenius norm [START_REF] Angeles | Fundamentals of Robotic Mechanical Systems: Theory, Methods and Algorithms[END_REF] is expressed as follows: Figure 6 depicts the inverse condition number of matrix A based on the Frobenius norm as a function of angles α and β . κ F (α, β ) is a minimum when its partial derivatives with respect to α and β vanish, namely,

κ F (α, β ) = 1 3 3S 2 αC 2 β + 1 S 2 αC 2 β (1 -S 2 αC 2 β ) (8)
κα (α, β ) = ∂ κ ∂ α = Cα(3S 2 αC 2 β -1)(S 2 αC 2 β + 1) 18S 3 αC 2 β (S 2 αC 2 β -1) 2 κ = 0 (9) κβ (α, β ) = ∂ κ ∂ β = - Sβ (3S 2 αC 2 β -1)(S 2 αC 2 β + 1) 18S 2 αC 3 β (S 2 αC 2 β -1) 2 κ = 0 ( 10
)
and its Hessian matrix is semi-positive definite. As a result, κ F (α, β ) is a minimum and equal to 1 along the hippopede curve, which is shown in Fig. 6 and defined by the following equation: 3S 2 αC 2 β -1 = 0 [START_REF] Yime | A novel 6-dof parallel robot with decoupled translation and rotation[END_REF] This hippopede curve amounts to the isotropic loci of the parallel spherical wrist. Figure 7 illustrates some placements of the actuated omni-wheels on the sphere leading to kinematically isotropic wheel configurations in the parallel spherical wrist. It should be noted that the three singular values of matrix A rω are equal to the ratio between the sphere radius R and the actuated omni-wheel radius r along the hippopede curve, namely, the velocity amplification factors of the PSW are the same and constant along the hippopede curve.

If the rotating sphere were to carry a camera, a laser or a jet of some sort, then the reachable orientations would be limited by interferences with the omni-wheels.

α = 35.26 • , β = 0 • α = 65 • , β = 50.43 • α = 50 • , β = 41.1 • α = 80 • , β = 54.11 •
Fig. 7: Kinematically isotropic wheel configurations in the parallel spherical wrist Therefore, a designer would be interested in choosing a small value of alpha, so as to maximize the field of view of the PSW. As a result, the following values have been assigned to the design parameters α and β :

α = 35.26 • (12) β = 0 • (13)
in order to come up with a kinematically isotropic wheel configuration in the parallel spherical wrist and a large field of view. The actuated omni-wheels are mounted in pairs in order to ensure a good contact between them and the sphere. A CAD modeling of the final solution is represented in Fig. 1.

Conclusion

This paper presents the novel concept of mounting a parallel spherical wrist in series with a CDPR, while preserving a fully-parallel actuation scheme. As a result, the actuators always remain fixed to the base, thus avoiding the need to carry electric power to the end-effector and minimizing its size, weight and inertia. Another original contribution of this article is the determination of the kinematically isotropic wheel configurations in the parallel spherical wrist. These configurations allow the designer to obtain a very good primary image of the design choices. To our knowledge, these isotropic configurations were never reported before, although several researchers have studied and used omni-wheel-actuated spheres. Future work includes the development of a control scheme to drive the end-effector rotations while accounting for the displacements of its centre, and also making a small scale prototype of the robot.

1 Fig. 3 :

 13 Fig. 3: Parameterization of the parallel spherical wrist

Fig. 4 :

 4 Fig. 4: (a) Actuation and constraint wrenches applied on the end-effector of the spherical wrist (b) Virtual i th leg with actuated prismatic joint

Fig. 5 :

 5 Fig. 5: Singular configurations of the parallel spherical wrist

Fig. 6 :

 6 Fig. 6: Inverse condition number of the forward Jacobian matrix A based on the Frobenius norm as a function of design parameters α and β


J P Tagutchou

Dr L Van De Steene

F J Escudero Sanz

S Salvador

Gasification of Wood Char in Single and Mixed Atmospheres of H 2 O and CO 2

Keywords: biomass, gasification, kinetics, mixed atmosphere, reactivity

In gasification processes, char-H 2 O and char-CO 2 are the main heterogenous reactions that are responsible for carbon conversion into H 2 and CO. These two reactions are generally looked at independently without considering interactions between them. The objective of this work was to compare kinetics of each reaction alone to kinetics of each reaction in a mixed atmosphere of H 2 O and CO 2 . A char particle was gasified in a macro thermo gravimetry reactor at 900 ı C successively in H 2 O/N 2 , CO 2 /N 2 , and H 2 O/CO 2 /N 2 atmospheres.

INTRODUCTION

The process of biomass conversion to syngas (H 2 C CO) involves a number of reactions. The first step is drying and devolatilization of the biomass, which leads to the formation of gas (noncondensable species), tar (gaseous condensable species), and a solid residue called char. Gas and tar are generally oxidized to produce H 2 O and CO 2 .

The solid residue (the subject of this work) is converted to produce syngas (H 2 C CO) thanks to the following heterogeneous reactions:

C C H 2 O ! CO C H 2 ;
(1)

C C CO 2 ! 2CO; (2) C C O 2 ! CO=CO 2 : (3)
Many studies have been conducted on char gasification in reactive H 2 O, CO 2 , or O 2 atmospheres. The reactivity of char during gasification processes depends on the reaction temperature and on the concentration of the reactive gas. Additionally, these heterogeneous reactions are known to be surface reactions, involving a so-called "reactive surface." While the role of temperature and reactive gas partial pressure are relatively well understood, clearly defining and quantifying the reactive surface remains a challenge. The surface consists of active sites located at the surface of pores where the adsorption/desorption of gaseous molecules takes place. The difficulty involved in determining this surface can be explained by a number of physical and chemical phenomena that play an important role in the gasification process:

(i) The whole porous surface of the char may not be accessible to the reactive gas, and may itself not be reactive. The pore size distribution directly influences the access of reactive gas molecules to active sites [START_REF] Roberts | A kinetic analysis of coal char gasification reactions at high pressures[END_REF]. It has been a common practice to use the total specific surface area measured using the standard BET test as the reactive surface. However, it has been established that a better indicator is the surface of only pores that are larger than several nm or tens of nm [START_REF] Commandré | The high temperature reaction of carbon with nitric oxide[END_REF]. (ii) As the char is heated to high temperatures, a reorganization of the structure occurs. The concentration of available active sites of carbon decreases and this has a negative impact on the reactivity of the char. This phenomenon is called thermal deactivation. (iii) The minerals present in the char have a catalytic effect on the reaction and help increase the reactivity of the char. Throughout the gasification process, there is a marked increase in the mass fraction of catalytic elements contained in the char with a decrease in the mass of the carbon.

Due to the complexity of the phenomena and the difficulty to distinguish the influence of each phenomenon on reactivity, a surface function (referred to as SF in this article) is usually introduced in models to describe the gasification of carbon and to globally account for all of the physical phenomenon [START_REF] Sorensen | Determination of reactivity parameters of model carbons, cokes and flame-chars[END_REF][START_REF] Gobel | Dynamic modelling of char gasification in a fixed-bed[END_REF].

While single H 2 O and CO 2 atmospheres have been extensively studied, only a few authors have studied the gasification of a charcoal biomass in mixed atmospheres.

Kinetic model classically proposed for the gasification of carbon residues is as follows:

d m.t/ dt D R.t/:m.t/: (4)
The reactivity of charcoal with a reactant j is often split into intrinsic reactivity r j , which only depends on temperature T and partial pressure p of the reactive gas, and the surface function F: R.t/ D F .X.t//:r j .T:p/:

(5)

As discussed above, the surface function F depends on many phenomena. In a simplifying approach, many authors express it as a function of the conversion X.

METHODOLOGY

Using a thermogravimetry (macro-TG) apparatus, gasification of char particles was characterized in three different reactive atmospheres: single H 2 O atmosphere, single CO 2 atmosphere, and a mixed atmosphere containing both CO 2 and H 2 O.

Experimental Set-up

The macro-TG reactor used in this work is described in detail in [START_REF] Mermoud | Influence of the pyrolysis heating rate on the steam gasification rate of large wood char particles[END_REF] N 2 -at a controlled temperature. The particles are continuously weighed to monitor conversion of the charcoal.

The particles were left in the hot furnace swept by nitrogen and maintained until their weight stabilized, attesting to the removal of possible residual volatile matter or re-adsorbed species. The atmosphere then turned into a gasifying atmosphere, marking the beginning of the experiment.

Preparation and Characterization of the Samples

The material used in this study was charcoal from maritime pine wood chips. Charcoal was produced using a pilot scale screw pyrolysis reactor. The pyrolysis operating conditions were chosen to produce a char with high fixed carbon content, i.e., a temperature of 750 ı C, a 1 h residence time, and 15 kg/h of flow rate in a 200-mm internal diameter electrically heated screw. Based on previous studies, the heating rate in the reactor was estimated to be 50 ı C/min [START_REF] Fassinou | Pyrolysis of Pinus pinaster in a two-stage gasifier: Influence of processing parameters and thermal cracking of tar[END_REF].

After pyrolysis, samples with a controlled particle size were prepared by sieving, and the thickness of particles was subsequently measured using an electronic calliper. Particles with a thickness of 1.5 and 5.5 mm were selected for all the experiments. Table 1 lists the results of proximate and ultimate analysis of the charcoal particles. The amount of fixed carbon was close to 90%, attesting to the high quality of the charcoal. The amount of ash, a potential catalyzer, was 1.4%.

GASIFICATION OF CHARCOAL IN SINGLE ATMOSPHERES

Operating Conditions

All experiments were carried out at a temperature of 900 ı C and at atmospheric total pressure. For each gasifying atmosphere, the mole fraction was chosen to cover values encountered in industrial reactors; experiments were performed at respectively 10, 20, and 40% mole fraction, respectively, for both H 2 O and CO 2 . In order to deal with the variability of the composition of biomass chips, each experiment was carried out with three to five particles in the grid basket. Care was taken to ensure there was no interaction between the particles. Each experiment was repeated at least three times.

Results and Interpretations

From the mass m(t) at any time, the conversion progress X was calculated according to Eq. ( 6): where m 0 and m ash represent, respectively, the initial mass of the char and the mass of ash at the end of the process. Figure 2 shows the conversion progress versus time for all the experiments. For char-H 2 O experiments, good repeatability was observed. Before 50% conversion, dispersion was small (<5%), while after 50% conversion, it could reach 10%. An average gasification rate was calculated for each experiment at X D 0:5 as 0:5=t (in s 1 ). It was 2.5 times larger in 40% steam than in 10% steam.

X.t/ D m 0 m.t/ m 0 m ash ; (6)
For char-CO 2 experiments, much larger dispersion was observed. It is difficult to give an explanation for this result. The gasification rate was 2.4 times higher in 40% CO 2 than in 10% CO 2 . Moreover, the results revealed a strange evolution in 20% CO 2 : the reaction was considerably slowed down after 60% conversion. This was also observed by [START_REF] Standish | Gasification of single wood charcoal particles in CO 2[END_REF] during their experiments on gasification of charcoal particles in CO 2 at a concentration of 20% CO 2 .

At a given concentration (for instance 40%) steam gasification was on average three times faster than CO 2 gasification.

Determination of Surface Functions (SF)

In practice, the SF can be derived without using a model by plotting R=R 50 (where R 50 is the reactivity for X D 50%). The reactivity R was obtained by derivation of the X curves. It was not possible to plot the values of SF when X tends towards 1 because by the end of the experiment, the decrease in mass was very small leading to a too small signal/noise ratio to enable correct derivation of the signal and calculation of R. At the beginning of the experiments, the derivative was also too noisy for accurate determination. Thus, for small values of X ranging from zero to 0.15, F .X/ was assumed to be constant and equal to F .X D 0:15/. In addition, from a theoretical point of view, F .X/ should be determined using intrinsic values of R, i.e., from experiments in which no limitation by heat or mass transfer occurs. In practice, it has been shown in the literature that experiments with larger particles can be used [START_REF] Sorensen | Determination of reactivity parameters of model carbons, cokes and flame-chars[END_REF]. It is shown in Figure 3 that the results obtained for small particles (1.5 mm thickness) were similar to those for larger particles (5.5 mm thickness). All results are plotted as F .X/ versus X in Figure 4 for the two reactant gases. For the atmospheres with 10 and 40% CO 2 , it is interesting to note that good repeatability was obtained for the SF when the evolution of X over time showed bad repeatability. While the reactivity of the three samples differed, the SF remained the same. Conversely, in 20% CO 2 , the repeatability of the test appeared to be good in the X D f .t/ plot (Figure 2), but results led to quite different shapes for the SF after 60% conversion.

An average value for repeatability experiments was then determined and is plotted in Figure 5. From these results, polynomials were derived for F .X/, as shown in Table 2. It was clearly observed that the 5th order was the most suitable to fit simultaneously all the experimental results of F .X/ in the different atmospheres with the best correlation coefficients. The results show that except in 20% CO 2 , the SF are monotonically increasing functions. For this representation, where the SF are normalized to 1 at X D 0:5, the plots indicate a small increase (from 0.6 to 1) when X increases from 0.1 to 0.5, and a very strong increase (to 4 or 5) when X tends towards 0.9. In experiments with 10, 20, and 40% H 2 O, the SF appeared not to be influenced by the concentration of steam. When CO 2 was the gasifying agent, a strong influence of the concentration was observed, confirming the strange behavior observed in Figure 2 in 20% CO 2 . The function for 10% CO 2 was similar to that of H 2 O (whatever the concentration).

A decreasing SF was found with 20% CO 2 for X between 0.6 and 0.75. This evolution has never previously been reported in the literature. Referring to the discussion about the phenomena that are taken into account in the SF, it is not possible to attribute this irregular shape to a physical phenomenon.

Figure 6 plots several SF from the literature, normalized at X D 0:5 to enable comparison. Expressions, such as ˛-order of .1 X/, and polynomial forms commonly used for biomass were retained. The SF obtained in 10% H 2 O, which is similar to that obtained in 40% CO 2 , has been added in the figure. It can be observed that up to 50% conversion, most of the SF published in the literature are similar. At higher conversions, all SF follow an exponential type function, but differ significantly in their rate of increase. The results of the authors' experiments (10% H 2 O) are within the range of values reported in the literature.

GASIFICATION OF CHARCOAL IN H 2 O C CO 2 ATMOSPHERES

To investigate mixed atmospheres, experiments were conducted using 20% H 2 O with the addition of alternatively 10, 20, and 40% CO 2 . The results of conversion versus time are plotted in Figure 7. For each mixed atmosphere, the average results obtained in the single atmospheres are given as references. Rather good repeatability was observed. It can be seen that adding CO 2 to H 2 O accelerated steam gasification. Indeed, mixing, respectively, 10, 20, and 40% of CO 2 with 20% of H 2 O increased the rate of gasification by 20, 33, and 57%, respectively, compared to the rate of gasification in 20% H 2 O alone. This is a new result, since in the literature, studies on biomass gasification concluded on that steam gasification was inhibited by CO 2 [START_REF] Ollero | The CO 2 gasification kinetics of olive residue[END_REF]. In the 20% H 2 O C 10% CO 2 atmosphere, the average gasification rate was 0.745 10 3 s 1 , which is approximately equal to the sum of the gasification rates obtained in the two separate atmospheres: 0.740 10 3 s 1 . This was also the case for the mixed atmosphere 20% H 2 O C 20% CO 2 . In the 20% H 2 O C 40% CO 2 atmosphere, the average gasification rate was 1.19 10 3 s 1 , i.e., 20% higher than the sum of the gasification rates obtained in the two single atmospheres. In other words, cooperation between CO 2 and H 2 O led to unexpected behaviors. A number of considerations can help interpret this result.

First, the geometrical structure of the two molecules-polar and non-linear for H 2 O and linear and apolar for CO 2 -predestines them to different adsorption mechanisms on potentially different active carbon sites [START_REF] Slasli | Modelling of water adsorption by activated carbons: Effects of microporous structure and oxygen content[END_REF].

The presence of hydrophilic oxygen, such as [-O], at the surface of char leads to the formation of hydrogen bonds, which could hinder H 2 O adsorption and favor that of CO 2 [START_REF] Stoeckli | The characterization of microporosity in carbons with molecular sieve effects[END_REF]. In the same way, as it is a non-organic molecule, H 2 O can only access hydrophobic sites while CO 2 , which is an organic molecule, can access both hydrophilic and hydrophobic sites.

According to [START_REF] Stoeckli | The characterization of microporosity in carbons with molecular sieve effects[END_REF], due to constriction or molecular sieve effects, CO 2 molecules have access to micropores of materials while those of H 2 O, which are assumed to be bigger, do not.

For one of the previous reasons or for any other reason, CO 2 molecules can access internal micropores more easily than H 2 O molecules, and can therefore open certain pores, making them accessible to H 2 O molecules.

The assumption that H 2 O and CO 2 molecules reacted with different sites and that no competition occurred is not sufficient to explain the increase of 20% in the gasification rate under mixed atmospheres. Point 0 can be proposed as an explanation, but a more precise explanation requires further research work. [START_REF] Roberts | Char gasification in mixtures of CO 2 and H 2 O: Competition and inhibition[END_REF] recently concluded that CO 2 has an inhibitory effect on H 2 O gasification, in contradiction to the authors' results. It is believed that the conclusions of [START_REF] Roberts | Char gasification in mixtures of CO 2 and H 2 O: Competition and inhibition[END_REF] are valid in their experimental conditions only, and with a little hindsight may be called into question.

Figure 8 gives the plots of SF obtained with the three mixed atmospheres and for all repeatability tests. Again, the repeatability of experiments was excellent until X D 0:6; this attests to the good quality of experiments and confirms that the variations in SF after 60% conversion are due to specific phenomena. Figure 9 compares all the average SF obtained in mixed atmosphere. From these curves, it can be seen that the curve is similar when the amount of CO 2 was modified from 10 to 40%. Thus, an average 5th-order polynomial expression for mixed atmosphere is given in Eq. ( 7):

F .X/ D 130:14X 5 264:67X 4 C 192:38X 3 57:90X 2 C 7:28X C 0:25:

(7)

CONCLUSION

The gasification of wood char particles during gasification in three atmospheres, i.e., H 2 O, CO 2 , and H 2 O/CO 2 , was experimentally investigated. The formulation adopted enables to split the reactivity R.t/ into kinetic parameters, r j , and all physical aspects, i.e., reactive surface evolution, thermal annealing, catalytic effects, into a surface function SF, F .X/, as follows: The repeatability of the derived SF was always very good until X D 0:6, which attests to the good quality of the experiments. For higher values of X, significant dispersion was observed, despite the use of several particles for each experiment. The SF depends on the nature of the reactant gas, and-in the case of CO 2 -on the concentration of the gas. A SF that surprisingly decreased with increasing X in the range 0.6-0.75 was obtained with CO 2 atmosphere in this work.

d
An important result of this article is that the addition of CO 2 in a H 2 O atmosphere led to an acceleration of gasification kinetic. In a mixture of 20% H 2 O and 40% CO 2 , the gasification rate was 20% higher than the sum of the gasification rates in the two single atmospheres.

FIGURE 2

 2 FIGURE 2 Conversion progress versus time during gasification at 900 ı C in single atmospheres (10, 20, and 40% H 2 O and 10, 20, and 40% CO 2 ). (color figure available online)

FIGURE 3

 3 FIGURE 3 SF for the two cases of 1.5 mm and 5.5 mm particles in steam atmosphere. (color figure available online)

FIGURE 4

 4 FIGURE 4 SF for each experimental result obtained in a single atmosphere.

FIGURE 5

 5 FIGURE 5 Average SF obtained in each single atmosphere. (color figure available online)

FIGURE 7

 7 FIGURE 7 Experimental results obtained in mixed atmospheres (A: 10% H 2 O and 20% CO 2 ; B: 20% H 2 O and 20% CO 2 ; and C: 20% H 2 O and 40% CO 2 ). For each mixed atmosphere, the corresponding average experimental results for single atmospheres are shown in thick solid line (20% H 2 O single atmosphere) and in thick dashed lines (CO 2 single atmospheres). (color figure available online)

FIGURE 8

 8 FIGURE 8 SF obtained in different mixed atmospheres for all experimental repeatability tests.

FIGURE 9

 9 FIGURE 9 Average SF obtained in the different mixed atmospheres.

  and is presented in Figure1. It consists of positioning several charcoal particles in a grid basket inside the reactor at atmospheric pressure. The reactor is swept by the oxidizing agent-H 2 O or CO 2 in

FIGURE 1 Macro thermogravimetry experimental apparatus. (1) Electric furnace; (2) Quartz tube; (3) Extractor; (4) Preheater; (5) Evaporator; (6) Water feeding system; (7) Water flow rate; (8) Leakage compensation; (9) Suspension basket; (10) Weighing system; (T i ) Regulation thermocouples; (M i ) Mass flow meter.

TABLE 1

 1 Proximate and Ultimate Analysis of Charcoal from Maritime Pine Wood Chips

		Proximate Analysis, Mass %		Ultimate Analysis, Mass %
	M	VM (dry)	FC(dry)	Ash (dry)	C˙0.3%	H ˙0.3%	O ˙0.3%	N ˙0.1%	S ˙0.005%
	1.8	4.9	93.7	1.4	89.8	2.2	6.1	0.1	0.01

M: Moisture content; VM: Volatile matter; FC: Fixed carbon.

  m.t/ dt D R.t/:m.t/ with R.t/ D F .X.t//:r j .T:p/: