Dallas Costis

Nephelie Chatzidiakou

Agiatis Benardou

Claire Clivaz

John Cunningham

Meredith Dabek

Patricia Garrido

Elena Gonzalez-Blanco

Jurij Hadalin

HATII Lorna Hughes

Gerlinde Schneider

Walter Scholger

Maciej Maryl

Stavros Angelis

Dimitris Gavrilis

Panagiotis Karioris

Koraljka Kuzman

Marko Lukin

Tvrtko Zebec

Anne Joly

Manfred Thaller

Zoe Schubert

Costis Dallas

Susan Schreibman

Ingrida Kelpšienė

Marcin Werla

Michał Kozak

Robert Owain

European survey on scholarly practices and digital needs in the arts and humanities Digital Methods and Practices Observatory Working Group (DiMPO) Survey highlights EN

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2,177 respondents across

Digital humanists access research materials both on digital devices and in analogue form

Except for books, digital humanists access research resources more often in digital than in analogue form. Ranked in order of frequency, digital devices such as PCs and laptops are most often used to access scholarly articles, images, video, audio, maps, and less often archival holdings and books. But nine out of ten digital humanists read books in print (compared to three out of five online), while more than half also access articles and archival holdings in analogue form. In tandem, three out of five respondents use a mobile device, such as a tablet, to consult images, video and audio resources while two out of five for research articles, books or maps.

More than two out of five digital humanists use a mobile device to consult most kinds of research resources

Digital humanists use digital methods or tools across the research lifecycle

Respondents reported using digital methods or tools to support all phases of the research lifecycle, from discovery to publication. However, while most respondents use them to discover, collect or create research assets, a smaller percentage reports using them for other purposes. Only about two out of three respondents reported use of digital methods or tools to annotate, enrich, or curate research assets.

Between 10-15% of respondents reported very frequent use of open access journals or publications, institutional portals and repositories, personal blogs or websites, and scholarly communities such as Academia and Resear-chGate, to disseminate their work. A larger percentage, between 35-45%, use this 'tetrad' of dissemination channels regularly. On the other hand, eight out of ten state that they have used open content journals or publication, albeit seldom. In addition, two out of ten respondents say they use regularly social media networks to disseminate their research. Less than one out of ten state that they use regularly generic online content services, such as Slideshare, Flickr or Youtube. Online library catalogues, digital collections and data repositories, and online journals are frequently consulted

Almost half of digital humanists use regularly a 'tetrad' of digital scholarly dissemination channels

Digital humanities researchers engage regularly in collaborative research

One out of three respondents indicate that they collaborate very often with others on a research project. Altogether, seven out of ten say that they engage often or very often in research collaboration. Only a very small fractionless than one out of fifteenstate that they never collaborate in research.

Frequency of collaborating with others on a research project. N= 2135

Frequency of accessing primary sources outside one's country of residence. N= 2136

The majority often use primary sources from abroad, but native tongue persists as the primary language of publication One out of five respondents access primary sources outside of their country of residence very often, and more than half do so often.

Only one in seven never uses primary sources from outside their country.

On the other hand, when asked to rank the languages which they use for scholarly publication, seven out of ten digital humanists identify their native language as their primary language of publication, while only one quarter identify English as the primary language. Nevertheless, the great majorityfour out of fivedo include English as a second publication language. In addition, almost one out of five suggest that they use another language for scholarly publication, as one of their first two choices. A additional three quarters of respondents, bringing the total to nine out of ten, state that they publish in another language beside their own and English as a third choice.

Publishing language. N= 1773

Improved findability of digital resources and digitization of non-digital ones are most highly valued

Asked to rate the importance of different needs in a scale from 1 to 10, three quarters of digital humanists rated Word processors and spreadsheets are the most common applications used to store and manage research assets

The full report and publications

A multi-authored report presenting the descriptive findings of the 2015 survey, as well as a journal paper, is compiled by members of the Digital Methods and Practices Working Group (DiMPO). The report, and further publications, present the consolidated and comparative findings of the survey, as well as selective country profiles. In addition, contributors from particular countries author publications on findings related to their country, and also in their national language.

  or laptop PC, more often than in printed or analogue format Use of desktop/laptop PC, mobile devices, and print or analogue devices to consult research material. N= 2177 …with the exception of books and archival items

  improved findability and access to existing digital research resources or data as the most important, with a score exceeding 9.5 out of 10. A slightly lower score of 9 was granted to digitization of research resources or data currently not in digital form by three out of four respondents. Two other needs, improved findability and access to digital tools or software, and networking with other researchers, research groups and institutions, share third place with a score exceeding 7 by more than three out of four respondents. Other functions, such as technical support on digital infrastructures, tools or software, online advice and information on using digital methods and tools for research, courses or workshops on how digital humanities methods and tools provide help in the course of the research, and online support from archivists, curators and/or librarians are also valued, but with a lower score.

  and analysis C. Dallas & N. Chatzidiakou 3. Consolidated findings N. Chatzidiakou & C. Dallas 4. Country profile: Austria G. Schneider & W. Scholger 5. Country profile: Greece N. Chatzidiakou & C. Dallas 6. Country profile: Lithuania I. Kelpšienė 7. Country profile: Poland M. Maryl 8. Country profile: Serbia T. Tasovac & N. Chatzidiakou 9. Country profile: Switzerland B. Immenhauser 10. Comparative findings All authors 11. Conclusions C. Dallas

Word processors and spreadsheets are the most common applications used to store and manage research assets 89,70% 60,60% 38,30% 33,70% 32,40% 16,70%

  Purpose of use of digital methods or tools. N=2176

	87,10% When working online, almost all 78,50% 80% 100% 90% respondents use web search very 50% 70% frequently to find research assets. 60% Nine out of ten reported frequent use	65,50%	73,30%	75,40%
	40% of online library catalogues, and
	10% 30% slightly less of digital archives, 20% collections or repositories, and online
	0% journals. Only seven out of ten use To discover, collect, or create my research assets To organize, structure, or manage my research assets academic search engines (such as Google Scholar) regularly. More than enrich, or curate To annotate, my research assets two out of five respondents say they	To process, analyze, or visualize my research assets	To publish, disseminate, or communicate about my
	use all these methods very frequently.				research
	On the other hand, frequent use of
	social media networks for resource
	discovery is reported by only one out
	of seven respondents.
	100%
	90%
	80%
	70%
	60%
	50%
	40%
	30%
	20%
	10%
	0%
	A word	A spreadsheet	Some non-	A note-taking	A database	A web-based
	processor	application	digital method	application	management	CMS
							system
							Means of dissemination of scholarly work. N=2132

For storage and management of research assets, nine out of ten respondents reported using a word processor. Three out of five respondents stated they use spreadsheets, while about one third said they use database management systems, or note-taking and bibliographic citation management applications. Only one out of seven presently use web-based content management systems (CMS) to store and manage research assets.

Frequency of use of services. N= 1452 Use of applications to store and manage research assets. N= 2176

Table of contents

 of Importance of digital infrastructure affordances. N= 2077

This work is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.

Scholarly practices survey: scope, objectives and plans Digital Methods and Practices Observatory Working Group (DiMPO)

  For further information or to join please contact the WG chair, Prof. Costis Dallas (c.dallas@dcu.gr).

	The DARIAH Digital Methods and Practices	The European
	Observatory WG (DiMPO) aims to develop and
	provide an evidence-based, up-to-date, and
	pragmatically useful account of the emerging
	information practices, needs and attitudes of arts and
	humanities researchers in the evolving European
	digital scholarly environment, for the benefit of the
	digital humanities research community. It seeks to
	achieve this objective through the inception of a
	longitudinal mixed methods research and monitoring
	programme on the information practices and
	scholarly methods employed in digitally-enabled arts
	and humanities work across Europe, and through the
	digital dissemination, validation and enrichment of
	research outcomes by the scholarly community.

survey on scholarly practices and digital needs in the arts and humanities is

  the outcome of collaborative work of European researchers from different countries, working within the DiMPO Working Group. It has been designed as a multiregional longitudinal survey, to be conducted online across European countries and to be repeated every few years. Its aim is to provide an evidencebased outlook of scholarly practices, needs and attitudes of European humanities researchers towards digital resources, methods and tools across space and time. Results of the first run of the survey (completed in March 2015) are presented in a multiauthored report, which includes comparative and consolidated analyses, as well as six country profiles. A new run is planned for 2017-18. For more information, see bit.ly/scholarlypractices.


Sylvain Rassat

Caroline Font

Aurélien Bolo

Sylvain Mazet

Guillaume Hulin

Alexia Fontaine

Emmanuelle Collado

Estelle Belay

THE CSNE (Canal Seine-Nord Europe) PROJECT

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

THE CSNE (Canal Seine-Nord Europe) PROJECT

In order to deal with the important amount of results, a data management system has been created with a specific architecture to store.

During the evaluation phase, all the archaeological data are recorded with a GPS.

Studies are the result of the collaboration between archaeologists and GIS operators.

New support (PC Tablet) of recording are tested directly on the field in an Access™ database.

All the archaeological data are stored in a database and linked to ArcGIS™. The GIS structure begins in AutoCAD Map™.

For a detailed study, micro topography can be realized using two GPS (Differential GPS).

Different scales of time and surface are aborded.

A new schema of working has been created in order to implicate every single actor in the archaeological process.

With old aerial photographies of the 1914-18 world war, archaeologists can anticipate the risk involved by this war.

  PHOTOGRAPHY

Inrap -Marc Talon (Project Master), Sylvain Rassat (Coordinator of the topographic, GIS and CAD team), Caroline Font (Coordinator of the GIS and CAD team), Aurélien Bolo (Land surveyor), Sylvain Mazet (Land surveyor), Guillaume Hulin (Geophysicist, CAD and GIS), Alexia Fontaine (CAD and GIS), Emmanuelle Collado (CAD), Estelle Belay (Publishing), Laurence-Garenne Marot (Publishing) Special thanks to Marc Talon, Pablo Ciezar (Inrap, AST), Gilles Prilaux (Inrap, AST), Alain Koehler (Inrap, DST) and all the CSNE archaeologists.


J Renotte

D Chablat
email: damien.chablat@irccyn.ec-nantes.fr

J Angeles
email: angeles@cim.mcgill.ca

THE DESIGN OF A NOVEL PRISMATIC DRIVE FOR A THREE-DOF PARALLEL-KINEMATICS MACHINE

The design of a novel prismatic drive is reported in this paper. This transmission is based on Slide-O-Cam, a cam mechanism with multiple rollers mounted on a common translating follower. The design of Slide-O-Cam was reported elsewhere. This drive thus provides pure-rolling motion, thereby reducing the friction of rack-and-pinions and linear drives. Such properties can be used to design new transmissions for parallel-kinematics machines. In this paper, this transmission is optimized to replace ball-screws in Orthoglide, a three-DOF parallel robot optimized for machining applications.

Introduction

In robotics and mechatronics applications, whereby motion is controlled using a piece of software, the conversion of motion from rotational to translational is usually done by ball screws or linear actuators. Of these alternatives, ball screws are gaining popularity, one of their drawbacks being the high number of moving parts that they comprise, for their functioning relies on a number of balls rolling on grooves machined on a shaft; one more drawback of ball screws is their low load-carrying capacity, stemming from the punctual form of contact by means of which loads are transmitted. Linear bearings solve these drawbacks to some extent, for they can be fabricated with roller bearings, their drawback being that these devices rely on a form of direct-drive motor, which makes them expensive to produce and to maintain. A novel transmission, called Slide-O-Cam, was introduced in [START_REF] González-Palacios | The novel design of a pure-rolling transmission to convert rotational into translational motion[END_REF] (Fig. 1) to transform a rotation into a translation. Slide-O-Cam is composed of four major elements: (i) the frame, (ii) the cam, (iii) the follower and (iv) the rollers. The input axis on which the cam is mounted, the camshaft, is driven at a constant angular velocity. Power is transmitted to the output, the translating follower, which is the roller-carrying slider, by means of purerolling contact between cam and roller. The roller comprises two components, the pin and the bearing. The bearing is mounted at one end of the pin, while the other end is press-fit into the rollercarrying slider. Contact between cam and roller thus takes place at the outer surface of the bearing. The mechanism uses two conjugate cam-follower pairs, which alternately take over the motion transmission to ensure a positive action; rollers are driven by the cams, throughout a complete cycle. The main advantage of using a cam-follower mechanism instead of an alternative transmission to transform rotation into translation is that contact through a roller reduces friction, contact stress and wear. This transmission will be optimized to replace the three ball screws used by the Orthoglide prototype [START_REF] Chablat | Architecture Optimization of a 3-DOF Parallel Mechanism for Machining Applications, the Orthoglide[END_REF]. Orthoglide features three prismatic joints mounted orthogonaly, three identical legs and a mobile platform, which moves in the Cartesian x-y-z space with fixed orientation, as shown in Fig. 2. The motor used to move each axis is SANYO DENKI (ref. P30B08075D) with a constant torque of 1.2 Nm from 0 to 3000 rpm. This property enables the mechanism to move throughout the workspace a 4 kg load with an acceleration of 17 ms -2 and a velocity of 1.3 ms -1 . On the ball screws, the pitch is 50 mm per cam turn. The minimum radius of the camshaft is 8.5 mm. Unlike Lampinen [START_REF] Lampinen | Cam shape optimisation by genetic algorithm[END_REF], who used a genetic algorithm, we use a deterministic method, while taking into account geometric and machining constraints as outlined in [START_REF] Bouzakis | Computer-Aided Optimum Design and NC Milling of Planar Cam Mechanims[END_REF]. In section 2, we introduce the relations describing the cam profile and the mechanism kinematics. In Section 3, we derive conditions on the design parameters so as to have a fully convex cam profile, to avoid undercutting, and to have a geometrically feasible mechanism. In Section 4, the pressure angle, a key performance index of cam mechanisms, is studied in order to choose the design parameters that give the best pressure-angle distribution, a compromise being done with the accuracy of the mechanism.

Synthesis of the Planar Cam Mechanism

Let the x-y frame be fixed to the machine and the u-v frame be attached to the cam, as depicted in Fig. 3. O 1 is the origin of both frames, while O 2 is the center of the roller and C is the contact point between cam and roller. The geometric parameters The notation of this figure is based on the general notation introduced in [START_REF] Gonzáles-Palacios | Cam Synthesis[END_REF], namely, (i) p: the pitch, i.e., the distance between the center of two rollers on the same side of the follower; (ii) e: distance between the axis of the cam and the line of centers of the rollers; (iii) a 4 : radius of the roller bearing, i.e., the radius of the roller; (iv) ψ: angle of rotation of the cam, the input of the mechanism; (v) s: position of the center of the roller, i.e, the displacement of the follower, the output of the mechanism; (vi) µ: pressure angle; (vii) f: force transmitted from the cam to the roller. In this paper, p is set to 50 mm, in order to meet the Orthoglide specifications.

The above parameters as well as the contact surface on the cam, are determined by the geometric relations dictated by the Aronhold-Kennedy Theorem in the plane [START_REF] Waldron | Kinematics, Dynamics, and Design of Machinery[END_REF]. When the cam makes a complete turn (∆ψ = 2π), the displacement of the roller is equal to p, the distance between two rollers on the same side of the roller-carrying slider (∆s = p). Furthermore, if we consider the initial configuration of the roller as depicted in Fig. 4, the roller is on the lower side of the x-axis for ψ = 0, so that we have s(0) = -p/2. Hence, the input-output function s is

s(ψ) = p 2π ψ - p 2 (1)
The expression for the first and second derivatives of s(ψ) with respect to ψ will be needed:

s ′ (ψ) = p/(2π) and s ′′ (ψ) = 0 (2)
The cam profile is determined by the displacement of the contact point C around the cam. The Cartesian coordinates of this point in the u-v frame take the form [START_REF] Gonzáles-Palacios | Cam Synthesis[END_REF]

u c (ψ) = b 2 cos ψ + (b 3 -a 4 ) cos(δ -ψ) (3a) v c (ψ) = -b 2 sin ψ + (b 3 -a 4 ) sin(δ -ψ) (3b)
with coefficients b 2 , b 3 and δ given by

b 2 = -s ′ (ψ) sin α 1 (4a) b 3 = (e + s ′ (ψ) sin α 1 ) 2 + (s(ψ) sin α 1 ) 2 (4b) δ = arctan -s(ψ) sin α 1 e + s ′ (ψ) sin α 1 (4c)
where α 1 is the directed angle between the axis of the cam and the translating direction of the follower; α 1 is positive in the ccw direction. Considering the orientation adopted for the input angle ψ and for the output s, as depicted in Fig. 3, we have

α 1 = -π/2 (5)
We now introduce the nondimensional design parameter η, which will be extensively used:

η = e/p (6)
Thus, from Eqs. (1), ( 2), (4a-c), ( 5) and ( 6), we compute the expressions for coefficients b 2 , b 3 and δ as

b 2 = p 2π (7a) b 3 = p 2π (2πη -1) 2 + (ψ -π) 2 (7b) δ = arctan ψ -π 2πη -1 (7c)
whence a first constraint on η, η = 1/(2π), is derived. An extended angle ∆ is introduced [START_REF] Lee | Design for Manufacturability of Speed-Reduction Cam Mechanisms[END_REF], so that the cam profile closes. Angle ∆ is obtained as the root of the equation v c (ψ) = 0. In the case of Slide-O-Cam, ∆ is negative, as shown in Fig. 5. Consequently, the cam profile closes within ∆ ≤ ψ ≤ 2π -∆.

O 1 x y u v C ψ (a) ψ = ∆ O 1 x y u v C ∆ (b) ψ = 0 O 1 x y C -u -v (c) ψ = π O 1 x y C ψ u v (d) ψ = 2π -∆ Figure 5. Extended angle ∆

Pitch-Curve Determination

The pitch curve is the trajectory of the center O 2 of the roller, distinct from the trajectory of the contact point C, which produces the cam profile. The Cartesian coordinates of point O 2 in the x-y frame are (e, s), as depicted in Fig. 3. Hence, the Cartesian coordinates of the pitch-curve in the u-v frame are

u p (ψ) = e cos ψ + s(ψ) sin ψ (8a) v p (ψ) = -e sin ψ + s(ψ) cos ψ (8b)

Geometric Constraints on the Mechanism

In order to lead to a feasible mechanism, the radius a 4 of the roller must satisfy two conditions, as shown in Fig. 6a: • Two consecutive rollers on the same side of the roller-carrying slider must not be in contact. Since p is the distance between the center of two consecutive rollers, we have the constraint 2a 4 < p. Hence the first condition on a 4 :

a 4 /p < 1/2 (9)
• The radius b of the shaft on which the cams are mounted must be taken into consideration. Hence, we have the constraint a 4 + b ≤ e, the second constraint on a 4 in terms of the parameter η thus being

a 4 /p ≤ η -b/p (10)
Considering the initial configuration of the roller, as depicted in Fig. 4, the v-component of the Cartesian coordinate of the contact point C is negative in this configuration, i.e., v c (0) ≤ 0. Considering the expression for v c (ψ) and for parameters b 3 and δ given

p 2πa 4 (2πη -1) 2 + (-π) 2 -1 sin arctan -π 2πη -1 ≤ 0
Further, we define A and B as:

A = p 2πa 4 (2πη -1) 2 + π 2 -1 and B = sin arctan -π 2πη -1 Since (2πη -1) 2 > 0, we have, (2πη -1) 2 + π 2 > π (11)
Hence, A > p/(2a 4 ) -1. Furthermore, from the constraint on a 4 , stated in Eq. ( 9), we have p/(2a 4 ) -1 > 0, whence A > 0.

Consequently, the constraint v c (0) ≤ 0 leads to the constraint B ≤ 0. We rewrite the expression for B, by using the trigonometric relation,

B ≤ 0 ⇐⇒ -π (2πη -1) 1 + π 2 /(2πη -1) 2 ≤ 0 which holds only if 2πη -1 > 0. Finally, the constraint v c (0) ≤ 0 leads to a constraint on η: η > 1/(2π) (12)

Pressure Angle

The pressure angle is defined as the angle between the common normal at the cam-roller contact point C and the velocity of the follower [START_REF] López-Cajún | Optimization of Cam Mechanisms[END_REF], as depicted in Fig. 3, where the presure angle is denoted by µ. This angle plays an important role in cam design. The smaller |µ|, the better the force transmission. In the case of high-speed operations, i.e., angular velocities of cams exceeding 50 rpm, the recommended bounds of the pressure angle are within 30 • . Nevertheless, as it is not always possible to have a 3

Copyright © 2004 by ASME pressure angle that remains below 30 • , we adopt the service factor, which is the percentage of the working cycle with a pressure angle within 30 • [START_REF] Lee | Design for Manufacturability of Speed-Reduction Cam Mechanisms[END_REF]. The service angle will be useful to take into consideration these notions in the ensuing discussion, when optimizing the mechanism.

For the case at hand, the expression for the pressure angle µ is given in [START_REF] López-Cajún | Optimization of Cam Mechanisms[END_REF] as

µ = arctan s ′ (ψ) -e s(ψ)
Considering the expressions for s and s ′ , and using the parameter η given in Eqs. ( 1), (2a) and ( 6), respectively, the expression for the pressure angle becomes

µ = arctan 1 -2πη ψ -π (13)
We are only interested in the value of the pressure angle with the cam driving the roller, which happens with

π ≤ ψ ≤ 2π -∆ (14)
Indeed, if we start the motion in the initial configuration depicted in Fig. 5b, with the cam rotating in the ccw direction, the cam begins to drive the roller only when ψ = π; and the cam can drive the follower until contact is lost, i.e., when ψ = 2π -∆, as shown in Figs. 5c &d. Nevertheless, as shown in Fig. 7, the conjugate cam can also drive the follower when 0 ≤ ψ ≤ π -∆; there is therefore a common interval, for π ≤ ψ ≤ π -∆, during which two cams can drive the follower. In this interval, the conjugate cam can drive a roller with lower absolute values of the pressure angle. We assume that, when the two cams can drive the rollers, the cam with the lower absolute value of pressure angle effectively drives the follower. Consequently, we are only interested in the value of the pressure angle in the interval,

π -∆ ≤ ψ ≤ 2π -∆ (15)
We study here the influence of parameters η and a 4 on the values of the pressure angle while the cam drives the roller, i.e., with π -∆ ≤ ψ ≤ 2π -∆, as explained above.

• Influence of parameter η: Figure 8 shows the influence of the parameter η on the pressure angle, with a 4 and p being fixed. From these plots we have one result: The lower η, the lower |µ|.

• Influence of the radius of the roller a 4 : a 4 does not appear in the expression for the pressure angle, but it influences the value of the extended angle ∆, and hence, the plot boundaries of the pressure angle, as shown in Fig. 7.

By computing the value of the extended angle ∆ for several values of a 4 , we can say that the higher a 4 , the lower |∆|. Consequently, since the boundaries to plot the pressure angle are π -∆ and 2π -∆, we can say that when we increase a 4 , -∆ decreases and the boundaries are translated toward the left, i.e., toward higher absolute values of the pressure angle.

Convexity of the Cam Profile and Undercutting

In order to enhance machining accuracy, we need the cam profile to be fully convex. In this section we establish conditions on the design parameters η and a 4 in order to have a fully convex cam profile. So, we study the sign of the curvature of the cam profile via that of the pitch curve. Furthermore, for cam design in roller-follower mechanisms, we should also consider undercutting. Undercutting occurs when the radius of the roller is greater than or equal to the minimum absolute value of the radius of curvature of the pitch curve. Upon avoiding undercutting, the sign of the curvature of the pitch curve is identical to that of the cam profile.

Curvature of the Cam Profile

The curvature of any planar parametric curve, in terms of the Cartesian coordinates u and v, and parameterized with any parameter ψ, is given by [START_REF] López-Cajún | Optimization of Cam Mechanisms[END_REF]:

κ = v ′ (ψ)u ′′ (ψ) -u ′ (ψ)v ′′ (ψ) [u ′ (ψ) 2 + v ′ (ψ) 2 ] 3/2 (16)
The sign of κ in Eq. ( 16) tells whether the curve is convex or concave at a point: a positive κ implies a convexity, while a negative κ implies a concavity at that point. To obtain the curvature of the cam profile for a given roller-follower, we use the Cartesian coordinates of the pitch curve, since obtaining its first and second derivatives leads to simpler expressions as compared with those associated with the cam profile itself. Then, the curvature of the cam profile is derived by a simple geometric relationship between the curvatures of the pitch curve and of the cam profile.

s(ψ) = p/(2π)ψ -p/2 , s ′ (ψ) = p/(2π) , s ′′ (ψ) = 0
With the above-mentioned expressions, we can compute the first and second derivatives of the Cartesian coordinates of the pitch curve with respect to the angle of rotation of the cam, ψ:

u ′ p (ψ) = ( s ′ (ψ) -e) sin ψ + s(ψ) cos ψ (17a) v ′ p (ψ) = ( s ′ (ψ) -e) cosψ -s(ψ) sin ψ (17b) u ′′ p (ψ) = (2s ′ (ψ) -e) cosψ -s(ψ) sin ψ (17c) v ′′ p (ψ) = -(2s ′ (ψ) -e) sin ψ -s(ψ) cosψ (17d)
By substituting η, η = e/p, along with Eqs. (17a-d), into Eq. ( 16), the curvature κ p of the pitch curve is obtained as

κ p = 2π p [(ψ -π) 2 + 2(2πη -1)(πη -1)] [(ψ -π) 2 + (2πη -1) 2 ] 3/2 (18)
provided that the denominator never vanishes for any value of ψ, i.e., provided that

η = 1/(2π) (19)
Let ρ c and ρ p be the radii of curvature of both the cam profile and the pitch curve, respectively, and κ c the curvature of the cam profile. Since the curvature is the reciprocal of the radius of curvature, we have ρ c = 1/κ c and ρ p = 1/κ p . Furthermore, due to the definition of the pitch curve, it is apparent that

ρ p = ρ c + a 4 (20)
Writing Eq. ( 20) in terms of κ c and κ p , we obtain the curvature of the cam profile as

κ c = κ p 1 -a 4 κ p ( 21
)
with κ p given in Eq. ( 18). As we saw previously, we want the cam profile to be fully convex, which happens if the pitch curve is fully convex too. We thus find first the convexity condition of the pitch curve.

Convexity Condition of the Pitch Curve

Considering the expression for κ p in Eq. ( 18), we have, for every value of ψ, κ p ≥ 0 if (2πη -1)(πη -1) ≥ 0 and η = 1/(2π), whence the condition on η:

κ p ≥ 0 if η ∈ [0, 1/(2π)[ ∪ [1/π, +∞[ (22)
Figure 9 shows pitch curve profiles and their curvatures for two values of η. The condition on η given in Eq. ( 22) must be

Undercutting Avoidance

We assume in this subsection that the pitch curve is fully convex, i.e., κ p ≥ 0 and η ≥ 1/π. In order to avoid undercutting, i.e., in order to have both the cam profile and the pitch curve fully convex, we need κ c to be positive. Considering the expression for the curvature of the cam profile κ c of Eq. ( 21), the condition to avoid undercutting is 1a 4 κ p > 0, whence the condition on the radius of the follower a 4 is

a 4 < 1 κ p (ψ) ∀ψ ∈ R
Since κ p is positive, this condition can be written as

a 4 < 1 κ pmax with κ pmax = max ψ∈R κ p (ψ) (24)
• Expression for κ pmax : In order to compute the expression for κ pmax , we need the first derivative κ ′ p of κ p with respect to ψ and its roots. With the condition η ≥ 1/π, the expression for κ p given in Eq. ( 18) is differentiable for every value of ψ. Thus, we obtain

κ ′ p = - 2π p (ψ -π)(ψ 2 -2πψ + π 2 + 4η 2 π 2 -10ηπ + 4) [(ψ -π) 2 + (2πη -1) 2 ] 5/2 (25)
The roots of κ ′ p are, apparently, ψ 1 = π and the roots ψ 2 and ψ 3 of the polynomial

P(ψ) = ψ 2 -2πψ + π 2 + 4η 2 π 2 -10ηπ + 4
Let β ψ be the discriminant of the equation P = 0, i.e.,

β ψ = -4η 2 π 2 + 10ηπ -4
Therefore, the sign of β ψ and, consequently, the roots ψ 2 and ψ 3 , depend on the value of η. Let β η be the discriminant of β ψ = 0, a quadratic equation in η. Hence, β η = 9π 2 , which is positive. The two roots of β ψ are 1/2π and 2/π. Thus,

β ψ > 0 if η ∈ [ 1 π , 2 π [ or β ψ < 0 if η ∈] 2 π , +∞[ β ψ = 0 if η = 2 π
We now study the roots of κ ′ p according to the value of η. • η ∈ [1/π, 2/π[: β ψ > 0, and the polynomial P has two roots ψ 2 and ψ 3 , so that κ ′ p has three roots:

ψ 1 = π (26a) ψ 2 = π + -4η 2 π 2 + 10ηπ -4 (26b) ψ 3 = π --4η 2 π 2 + 10ηπ -4 (26c)
• η ∈]2/π, +∞[: β ψ < 0, and the polynomial P has no real roots, so that κ ′ p has only one root, ψ 1 = π. • η = 2/π: β ψ = 0, and the polynomial P has one double root equal to π, so that κ ′ p has one triple root ψ 1 = π. To decide whether these roots correspond to minima or maxima, we need to know the sign of the second derivative κ ′′ p of κ p with respect to ψ, for the corresponding values of ψ. If the second derivative is negative, the stationary value is a maximum; if positive, a minimum. The expressions for the second derivatives were computed with Maple, for the values of ψ given in

κ ′′ p (ψ 1 ) = 4π(ηπ -2) p|2ηπ -1| 3 (2ηπ -1) κ ′′ p (ψ 2 ) = κ ′′ p (ψ 3 ) = 8π(ηπ -2) 9p(2ηπ -1) √ 6ηπ -3 • If η ∈ [1/π, 2/π[, κ ′′ p (ψ 1 ) > 0 and κ ′′ p (ψ 2 ) = κ ′′ p (ψ 3
) < 0, the curvature of the pitch curve has one local minimum for ψ 1 and two maxima, for ψ 2 and ψ 3 . Hence, the value of κ pmax is

κ pmax1 = κ p (ψ 2 ) = κ p (ψ 3 ) = 4π 3p √ 6ηπ -3 (27)
Figure 10a shows a plot of the pitch-curve curvature with η = 1/π and p = 50 mm. Since η is taken equal to the convexity limit 1/π, the curvature remains positive and only vanishes for

ψ = π. • If η ∈]2/π, +∞[, κ ′′ p (ψ 1
) < 0, the curvature of the pitch curve has a maximum for ψ 1 . Hence, the value of κ pmax is

κ pmax2 = κ p (ψ 1 ) = 4π p (2η 2 π 2 -3ηπ + 1) (4η 2 π 2 -4ηπ + 1) 3/2 (28)
Figure 9d shows a plot of the pitch-curve curvature with η = 0.7 (η > 2/π) and p = 50 mm.

• If η = 2/π, κ ′′ p (ψ 1 ) = 0, we cannot tell whether we are in the presence of a maximum or a minimum. We solve this uncertainty graphically, by plotting the curvature of the pitch curve for η = 2/π and p = 50 mm. Figure 10b reveals that the curvature has a maximum for ψ 1 . The value of this maximum can be obtained by substituting η by 2/π into either κ pmax1 or κ pmax2 , expressed in Eqs. ( 27) and (28), respectively.

In summary, to have a fully convex cam profile, taking the geometric constraints on the mechanism into consideration, parameter η must obey the condition given in Eq. ( 23), i.e. η ≥ 1/π. We combine the condition on a 4 to avoid undercutting, as given in Eq. ( 24), with the geometric constraints on the mechanism, as given in Eqs. ( 9) and [START_REF] Renotte | The Design of a Pure-Rolling Ca Mechanism to Convert Rotationnal into Translational Motion[END_REF], which are, respectively, a 4 /p < 1/2 and a 4 /p ≤ ηb/p:

if η ∈ [ 1 π , 2 π ], a 4 < min 1 κ pmax1 , p 2 , ηp -b (29a) 6 Copyright © 2004 by ASME if η ∈ [ 2 π , +∞[, a 4 < min 1 κ pmax2 , p 2 , ηp -b (29b)
where κ pmax1 and κ pmax2 are given in Eqs. ( 27) and ( 28), respectively.

Optimization of the Roller Pin

We concluded in previous section that the lowest values of parameters η and a 4 led to the lowest values of the pressure angle. Nevertheless, we must take into consideration that the smaller the radius of the roller, the bigger the deformation of the roller pin, and hence, a decrease of the stiffness and the accuracy of the mechanism. In this section we formulate and solve an optimization problem to find the best compromise on parameters η and a 4 to obtain the lowest pressure angle values with an acceptable deformation of the roller pin.

Minimization of the Elastic Deformation on the

Roller Pins Here we find the expression for the maximum elastic deformation on the pin, which will be minimized under given constraints. Figure 11 displays the free part of the pin, i.e., the part not fixed to the roller-carrying slider, as a cantilever beam, where the load F = f 2

x + f 2 y denotes the magnitude of the force f transmitted by the cam. This force is applied at a single point at the end of the pin in the worst loading case. Although the dimensions of the pin are not those of a simple beam, we assume below that the pin can be modelled as such, in order to obtain an explicit formula for its deflection. This assumption was found to be plausible by testing it with FEA [START_REF] Teng | An optimality criterion for the structural optimization of machine element[END_REF]. The displacement v L at the free end of the pin turns out to be

v L = v 2 x + v 2 y = FL 3 3EI ( 30
)
where E is the Young modulus and I = πa 4 5 /4, with a 5 denoting the radius of the pin, is the polar moment of inertia of the cross section. Moreover, v x and v y are the pin elastic displacements in the x-and y-directions, respectively, at the free end.

Before proceeding, we prove that the vertical component f y of the transmitted force is constant, and hence, we will consider only the magnitude of the x-component of v L . Since we assume that the mechanism undergoes a pure-rolling motion, the force exerted by the cam onto the roller, denoted by f = [ f x f y ] T , passes through the center of the roller, i.e., its line of action passes through points O 2 and C, as depicted in Fig. 3

f y = 2πτ p = F 0 ( 31
)
Since τ is constant, f y is also constant throughout one cycle. Consequently we only have to consider the x-component of f, and hence, v x for the minimization problem:

v x = | f x |L 3 3EI = 4| f x |L 3 3Eπa 4 5 = β | f x | a 4 5 , β = 4L 3 3Eπ (32)
β thus being a constant factor. The objective function z, to be minimized, is thus defined as

z = f 2 max a 4 5 → min η,a 4 ,a 5 (33)
where f max is the maximum value of f x throughout one cycle. Since

f x = f y tan δ = F 0 tan δ (34)
we obtain

z = 1 a 4 5 max ψ f 2 x = 1 a 4 5 max ψ F 2 0 tan 2 δ = F 2 0 a 4 5 max ψ 1 tan 2 δ
with δ, a function of ψ, given in Eq. (7c). Moreover, the system operates by means of two conjugate mechanisms, which alternately take over the power transmission. We established in Eq. ( 15) that when one mechanism is in positive action, ψ is bounded between ψ i = π -∆ and ψ f = 2π -∆, which corresponds to δ bounded between δ i and δ f with 0 ≤ δ i < δ f ≤ π. Moreover, functions 1/ tan 2 δ and cos 2 δ are both unimodal in -π ≤ δ ≤ 0 and in 0 ≤ δ ≤ π, their common maxima finding themselves at -π, 0 and π. Since cos 2 δ is better behaved than 1/ tan 2 δ, we redefine z as

z = 1 a 4 5 max δ i ≤δ≤δ f cos 2 δ 7
Copyright © 2004 by ASME Furthermore, the function cos 2 δ attains its global minimum of 0 in [0, π], its maximum in the interval

[δ i , δ f ], included in [0, π],
occurring at the larger of the two extremes of the interval, δ i or δ f . It follows that the objective function to be minimized be-

comes z = 1 a 4 5 max cos 2 δ i , cos 2 δ f
with δ i and δ f the values of δ for ψ i = π -∆ and ψ f = 2π -∆, respectively. Using the expression for δ given in Eq. (7c) and the trigonometric identity

cos(arctan x) = 1 √ 1 + x 2
we obtain the expression for cos 2 δ:

cos 2 δ = (2πη -1) 2 (2πη -1) 2 + (ψ -π) 2 (35) Hence, cos 2 δ i = (2πη -1) 2 (2πη -1) 2 + (ψ i -π) 2 (36a) cos 2 δ f = (2πη -1) 2 (2πη -1) 2 + (ψ f -π) 2 (36b)
Furthermore, since

ψ i = π -∆, ψ f = 2π -∆ and ∆ < 0, we have ψ f > ψ i > π, ψ f -π > ψ i -π >
with cos 2 δ i given in Eq. (36a) and ψ i = π -∆.

Geometric Constraints

Two neighboring pins cannot be tangent to each other, as depicted in Fig. 12, and hence the radius a 5 of the pin is bounded as

a 5 /p < 1/4 (38)
Furthermore, a 4 and a 5 are not independent. From the SKF catalogue, for example, we have information on bearings available We define now two non-dimensional parameters α 4 and α 5 :

α 4 = a 4 /p α 5 = a 5 /p (40)
where α 5 can be derived from Eq. (39) as The optimization problem is now expressed as

z(η, α 4 ) = cos 2 δ i α 4 5 → min η,α 4 (42)
Moreover, we recall the geometric constraint defined in Eqs. ( 23) and (29) that can be rewritten as

g 1 = 1 π -η ≤ 0 (43a) g 2 = α 4 - 1 2 < 0 (43b) g 3 = α 4 - 1 pκ pmax < 0 (43c) g 4 = α 4 -η + b p ≤ 0 (43d) g 5 = α 5 - 1 4 < 0 (43e)
with cos 2 δ i and α 5 given in Eqs. (36a) and (41), respectively.

8

Copyright © 2004 by ASME

Results of the Optimization Problem

We solve the foregoing optimization problem with an algorithm implemented Matlab, using p = 50 mm and b = 9.5 mm. One solution is found, corresponding to η = 0.69 and a 4 = 24.9992 mm, with a value of z = 249. The algorithm finds the values of η and a 4 as big as possible considering the constraints. For this solution, constraints (43d & e) are active. Nevertheless, as we saw in subsection 3.3. about the influence of parameters h and a 4 , we want these parameters to be as small as possible in order to have low pressure-angle values. For the solution found above, the service factor is equal to 0%. Consequently, we must find a compromise between the pressure angle and the roller-pin elastic deformation. Table 1 shows solutions found by the optimization algorithm upon reducing the boundaries of η. Each time the algorithm finds the corresponding value of a 4 as big as possible, constraint (43d) becomes active. Recorded in this table is also the corresponding maximum elastic deformation of the roller pin v Lmax (its expression is derived below), the minimum and the maximum absolute values of the pressure angle, |µ min | and |µ max |, respectively, and the service factor, as defined in section 2.4. From Eqs. ( 30) and (32) we have

v L = β a 4 5 f 2 x + f 2 y
Using Eqs. ( 31) and (34), the above equation leads to

v L = βF 0 a 4 5 1 + 1 tan 2 δ
Which can be simplified by means of the expression for cos 2 δ i given in Eq. (36a) as

v Lmax = βF 0 a 4 5 (2πη -1) 2 + (ψ i -π) 2 |ψ i -π| (44)
with β, F 0 and a 5 given in Eqs. (32), ( 31) and (39), respectively, and

ψ i = π -∆.

A Non-Coaxial Conjugate-Cam Mechanism

This Section describes a new mechanism, based on Slide-O-Cam, that enables us to decrease considerably the pressure angle while meeting the Orthoglide specifications. This mechanism is composed of three conjugate cams mounted on three parallel shafts, the rollers being placed on one single side of the roller-carrying slider. One motor provides the torque to the central camshaft, this torque then being transmitted to the two other camshafts through a parallelogram mechanism coupling them, whose detailed design is reported in [START_REF] Renotte | The Design of a Pure-Rolling Ca Mechanism to Convert Rotationnal into Translational Motion[END_REF]. We denote by 1, 2 and 3 the three cams, as shown in Fig. 14. The profile of each cam is described in Section 2. The cams are mounted in such a way that the angle between the u-axis of cam 1 and cam 2 is 120 • , and the angle between the u-axis of cam 1 and cam 3 is 240 • . According to the configuration of the mechanism depicted in Fig. 14, and denoting by y 12 and y 13 the distance between the origin of 1 and 2, and between the origin of 1 and 3, respectively, we have

y 12 = p/2 + p + s(2π/3) , y 13 = p/2 + 2p + s(4π/3)
Using the expression of the input-output function s given in Eq. (1), we obtain

y 12 = 4p/3 , y 13 = 8p/3 (45) 9
Copyright © 2004 by ASME Figure 15 shows the pressure angle variation for each cam vs. ψ where 1, 2 and 3 denote the plot of the pressure angle for cams 1, 2 and 3, respectively. Moreover, cams 2 and 3 are rotated by angles 2π/3 and 4π/3, respectively, from cam 1. We can also consider that the plot for cam 3 that drives the follower before cam 1 in a previous cycle, refereed to as 3' in Fig. 15, is a translation of -2π/3 from cam 1. As we saw in Eq. ( 14), cam 1 can drive the follower within π ≤ ψ ≤ 2π -∆, which corresponds in The above interval corresponds in Fig. 15 to the part of the plot 3' between points A and C. Consequently, there is a common part for cams 1 (plot 1) and 3 (plot 3') during which these two cams can drive the follower, namely, between points B and C, which corresponds to π ≤ ψ ≤ 4π/3 -∆. Moreover, during this common part, cam 3 has lower absolute pressure angle values than 1, and hence, we consider that only cam 3 drives the follower. Consequently, cam 1 drives the follower only within 4π/3 -∆ ≤ ψ ≤ 2π -∆. These boundaries allow us to have a pressure angle lower than with coaxial conjugate cams, since we do not use anymore the part of the cam profile within π -∆ ≤ ψ ≤ 4π/3 -∆, which has high absolute pressure angle values. We can thus obtain a higher service factor for the mechanism. The drive thus design is sketched in Fig. 16.

Conclusions

The non-coaxial conjugate-cam mechanism reported here allows us to drive the Orthoglide with prismatic actuators using rotary DC motors. Moreover, the maximum roller-pin deformation v Lmax derived in eq.( 44) is reasonable low. In

Figure 1 .

 1 Figure 1. Layout of Slide-O-Cam Figure 2. The Orthoglide

  Figure 3. Parameterization of Slide-O-Cam

Figure 4 .

 4 Figure 4. Initial configuration of the mechanism defining the cam mechanism are illustrated in the same figure.The notation of this figure is based on the general notation introduced in[START_REF] Gonzáles-Palacios | Cam Synthesis[END_REF], namely, (i) p: the pitch, i.e., the distance between the center of two rollers on the same side of the follower; (ii) e: distance between the axis of the cam and the line of centers of the rollers; (iii) a 4 : radius of the roller bearing, i.e., the radius of the roller; (iv) ψ: angle of rotation of the cam, the input of the mechanism; (v) s: position of the center of the roller, i.e, the displacement of the follower, the output of the mechanism; (vi) µ: pressure angle; (vii) f: force transmitted from the cam to the roller. In this paper, p is set to 50 mm, in order to meet the Orthoglide specifications.The above parameters as well as the contact surface on the cam, are determined by the geometric relations dictated by the Aronhold-Kennedy Theorem in the plane[START_REF] Waldron | Kinematics, Dynamics, and Design of Machinery[END_REF]. When the cam makes a complete turn (∆ψ = 2π), the displacement of the roller

Figure 6 .

 6 Constraints on the radius of the roller in Eqs. (3b), (7b & c), respectively, the above relation leads to the condition:

Figure 7 .Figure 8 .

 78 Figure 7. Pressure angle distribution

4

  Copyright © 2004 by ASME The Cartesian coordinates of the pitch curve were recalled in Eqs. (8a & b), while Eqs. (2a & b) give their first and second derivatives

Figure 9 .

 9 Figure 9. Concave (a) and convex (b) pitch curve profiles and their corresponding curvatures with p = 50 mm combined with the condition appearing in Eq. (12), η > 1/(2π); hence, the final convexity condition of the pitch curve is:

Figure 10 .

 10 Figure 10. Pitch-curve curvature for p = 50 mm Eqs. (26a-c):

Figure 11 .

 11 Figure 11. Approximation of the roller pin as a cantilever beam

  . With a constant torque τ provided by the motor, we have τ = ||f||d, where d denotes the distance from the center of the input axis to the line of action of the force f. Moreover, we have d = b 2 sin δ. Hence, τ = ||f||(b 2 sin δ) = b 2 (||f|| sin δ) = b 2 f y . Finally, since b 2 = 2π/p we obtain the expression for f y sought:

= cos 2 δ i a 4 5 →

 5 0 and, consequently, from Eqs. (36a & b), cos 2 δ i > cos 2 δ f and the objective function to minimize becomes z min η,a 4 ,a 5

p p/2 a 4 a 5 FigureFigure 13 .

 513 Figure 12. Geometric constraint on the rollerpin radius

α 5 = ( 5 / 8 )α 4 -

 5584 25/(8p) with p in mm. (41)

Fig. 15 to the part of the plot 1

 1 Figure15shows the pressure angle variation for each cam vs. ψ where 1, 2 and 3 denote the plot of the pressure angle for cams 1, 2 and 3, respectively. Moreover, cams 2 and 3 are rotated by angles 2π/3 and 4π/3, respectively, from cam 1. We can also consider that the plot for cam 3 that drives the follower before cam 1 in a previous cycle, refereed to as 3' in Fig.15, is a translation of -2π/3 from cam 1. As we saw in Eq. (14), cam 1 can drive the follower within π ≤ ψ ≤ 2π -∆, which corresponds in Fig.15to the part of the plot 1 between points B and D. Consequently, cam 2 can drive the follower withinπ + 2π/3 ≤ ψ ≤ 2π -∆ + 2π/3 i.e. 5π/3 ≤ ψ ≤ 8π/3 -∆ and cam 3 within π + 4π/3 ≤ ψ ≤ 2π -∆ + 4π/3 i.e. 7π/3 ≤ ψ ≤ 10π/3 -∆which is equivalent to saying that cam 3 can drive the follower in a previous cycle, within π -2π/3 ≤ ψ ≤ 2π -∆ -2π/3 i.e. π/3 ≤ ψ ≤ 4π/3 -∆

  Figure 15. Pressure angle for the three cams

Table 1 .

 1 In Table1we record the value of v Lmax with L = 10 mm, τ = 1.2 Nm (according to the Orthoglide specifications recalled in section 1) and E = 2 × 10 5 MPa. We conclude from Table1that for this cam profile we cannot find an acceptable compromise between a low deformation of the roller pin, and hence a high stiffness and accuracy of the mechanism, and low pressure-angle values. Indeed, for an acceptable deformation of the roller pin, v Lmax = 8.87 µm, obtained with η = 0.38, the service factor equals 54.68%, which is too low. On the other hand, for an acceptable service factor of 79.43%, obtained with η = 1/π, the deformation of the roller pin is equal to 710.19 µm. Results of the optimization problem, with p = 50 mm, b = 9.5 mm, L = 10 mm, τ = 1.2 Nm and E = 2 × 10 5 MPa

	η	a 4 (mm)	a 5 (mm)	z		v Lmax (µm)	|µ min | ( • )	|µ max | ( • )	service factor (%)
	0.69	24.99 12.50	249		0.09	42.11	80.68	0
	0.5	15.5	6.56	2968		0.50	28.59	69.81	6.85
	0.4	10.5	3.44	32183		4.32	20.31	57.99	46.68
	0.39	10	3.12	45490		6.07	19.46	56.42	50.68
	0.38	9.5	2.81	66659		8.87	18.61	54.78	54.68
	0.37	9	2.50	102171		13.63	17.75	53.04	58.69
	0.36	8.5	2.19	165896		22.31	16.89	51.22	62.69
	0.35	8	1.87	290765		39.71	16.03	49.31	66.70
	0.34	7.5	1.56	566521		79.18	15.17	47.31	70.72
	0.33	7	1.25	1.29 10 6	186.06 14.31	45.21	74.73
	1/π	6.41	0.88	4.68 10 6	710.19 13.31	42.64	79.43
		p	x, u p/2		s(2π/3)		s(4π/3)	v
	y, v		O 1
	1		2				3
			u	y 12	y 13	v			u

Figure 14. Layout of the non-coaxial conjugate-cam mechanism

Table 2

 2

	, we

Table 2 .

 2 Design parameters, roller pin deformation and pressure angle for the non-coaxial conjugate-cam mechanism, with p = 50 mm, b = 9.5 mm, L = 10 mm, τ = 1.2 Nm and E = 2 × 10 5 MPa.record the values of η, a 4 , a 5 , v Lmax , |µ min |, |µ max | and the service factor for the non-coaxial conjugate-cam mechanism. The best compromise is to use the non-coaxial conjugate-cam mechanism with η = 0.37, whence the radius of the roller is a 4 = 9 mm and the roller-pin deformation is v Lmax = 9.76 µm with a good service factor of 88.03%.


N Khélifa
email: khelifa@cnam.fr

Water vapour effects in mass measurement

Keywords: mass metrology, air density, water vapour

Water vapour inside the mass comparator enclosure is a critical parameter. In fact, fluctuations of this parameter during mass weighing can lead to errors in the determination of an unknown mass. To control that, a proposal method is given and tested. Preliminary results of our observation of water vapour sorption and desorption processes from walls and mass standard are reported.

Introduction

Water vapour contained in ambient air influences measurement in many field of science. In mass metrology, it is necessary to correctly evaluate air moisture and its changes during mass comparisons. In practice, the air density air ρ [kg m -3 ] is deduced, by using the so called "CIPM-1981/91 formula" for air density [START_REF] Davis | Equation for the determination of the density of moist air[END_REF], from the measured parameters of ambient air.

f M M v a air a v x T R Z M p ε ρ +             - - = 1 1
In this formula, a M and v M are the molar mass [kg mol -1 ] of respectively dry air and water, Z the compressibility factor, R the constant of ideal gases [J mol -1 K -1 ], p the atmospheric pressure [Pa], v

x the molar fraction of water vapor and = x are included [START_REF] Davis | Equation for the determination of the density of moist air[END_REF]. Recently, determination of air density from the results of artefacts comparisons in ambient air and in vacuum, show a significant difference against the value evaluated by the classical method (CIPM-1981/91 formula). This discrepancy is of the order of the fitting error of the CIPM formula, i.e. [START_REF] Picard | Mass comparisons using air buoyancy artefacts[END_REF][START_REF] Chung | Air density determination using 1 kg buoyancy mass comparisons[END_REF]. This observation needs further studies, particularly concerning the existing air density gradients inside the mass comparator chamber. In fact, sorption and desorption of water vapor by the mass standards and the walls of the chamber, during the weighing procedure induce fluctuations of air inside the enclosure.

4 10 7 0 - × , kg m -3

Air moisture measurement inside the enclosure

In practice the molar fraction of water vapor is calculated from the measurement of dew point temperature d t or from the relative humidity HR. In order to minimize air perturbations inside the chamber of the mass balance, the temperature of the dew point is measured only a long time before the start and at the end of a succession of weighing. During mass weighting, which takes several hours, sometime a capacitive hygrometer is used to evaluate the drift in air humidity. Here we use a method, based on molecular absorption in the near infrared, developed and assigned to follow the small changes of water vapour. The near-infrared laser diode device is described in a previous reports [START_REF] Khélifa | Capteur Optique pour le Contrôle de l'humidité de l'Air en Métrologie des Masses[END_REF][START_REF] Khélifa | Air Moisture Measurement : The Indiscreetness of the Dew-Point Hygrometer[END_REF]. Here, we use this sensor to confirm the indiscreet behaviour of the dew-point hygrometer and to observe water vapor sorption and desorption.

A schematic diagram of the experimental setup is represented by figure 1. The systems consist of a vacuum housing and an oil free pump associated to a turbo molecular pump. The working pressure range is between 1 Pa and standard atmosphere (10 5 Pa). The pressure inside the enclosure (vacuum pump shut off) goes from 1 Pa to 1800 Pa in about 120 minutes. Initial sorption and desorption processes within the vacuum is masked by the global leak. With the "made home" optical hygrometer, air moisture is monitored when air is progressively evacuated from the housing. The water vapor absorption is converted onto partial pressure. For that, the absorption signal is adjusted to the mean value of relative humidity measured, with a calibrated capacitive hygrometer, at the start of measurement. The changes of water vapor, when total pressure of moist air inside the chamber is progressively diminished by pumping are given in figure 3. As we can see, below a air pressure of about 80000 Pa, the water vapor decrease very slowly.

OFF ON

Dew-point hygrometer is switched : ON @ t = 58 min. and OFF @ t = 5 h 28 min.

Absorption measurement Capacitive measurement

Water vapour pressure (pascals) Time (hours)

Conclusion

In vacuum comparisons, supplementary correction must be made due to sorption process. The value of adsorbed mass per surface area depends on mass standard (material allow, surface roughness, …). In fact, a monolayer of adsorbed water vapor on the surface of a stainless steel kilogram standard corresponds to a mass variation of about 2 g µ . In mass comparisons, the effects of buoyancy in air and the adsorption of air molecules onto the surface of weight need to be considered.

1 -×

 1 error of the formula.The combined relative standard uncertainty of air density, for normal atmospheric conditions, is at the level of 4 10 kg m -3 , when uncertainties for p, T, a M and v

Fig. 1 .

 1 Fig. 1. Schematic diagram of experiment

Figure 2

 2 Figure 2 shows the changes of water vapor inside the enclosure during time. The air environmental parameters, are Pa p 101532 = , C , t °= 30 21 and a relative humidity HR = 52,8 %. The results show the perturbations induced by the dew point hygrometer and confirm the superiority of the optical device compared to the capacitive in terms of sensitivity.

Fig. 2 .

 2 Fig. 2. Evolution of relative humidity within total air pressure inside the housing.

Fig. 3 .

 3 Fig. 3. Variation of water vapor pressure as a function of total air pressure