ACOMPARISON of the number of independent actively. Design and Analysis of Kinematically Redundant Parallel Manipulators With Configurable Platforms

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1 IEEE TRANSACTIONS ON ROBOTICS, VOL 21, NO 3, JUNE Design and Analysis of Kinematically Redundant Parallel Manipulators With Configurable Platms Maher G Mohamed and Clément M Gosselin, Member, IEEE Abstract Redundancy can, in general, improve the ability and permance of parallel manipulators by implementing the redundant degrees of freedom to optimize a secondary objective function Almost all published researches in the area of parallel manipulators redundancy were focused on the design and analysis of redundant parallel manipulators with rigid (nonconfigurable) platms and on grasping hands to be attached to the platms Conventional grippers usually are not appropriate to grasp irregular or large objects Very few studies focused on the idea of using a configurable platm as a grasping device This paper highlights the idea of using configurable platms in both planar and spatial redundant parallel manipulators, and generalizes their analysis The configurable platm is actually a closed kinematic chain of mobility equal to the degree of redundancy of the manipulator The additional redundant degrees of freedom are used in reconfiguring the shape of the platm itself Several designs of kinematically redundant planar and spatial parallel manipulators with configurable platm are presented Such designs can be used as a grasping device especially irregular or large objects or even as a micro-positioning device after grasping the object Screw algebra is used to develop a general framework that can be adapted to analyze the kinematics of any general-geometry planar or spatial kinematically redundant parallel manipulator with configurable platm Index Terms Analysis, configurable platm, design, kinematic redundancy, parallel manipulator I INTRODUCTION ACOMPARISON of the number of independent actively controlled joints or actuators and the number of degrees of freedom (DOFs) required indicates whether a given kinematic structure can be considered redundant or not A redundant mechanism is a mechanism with more actuators than the required number of controlled degrees of freedom Redundancy in serial manipulators has been studied extensively [1] [7] In serial manipulators, the redundancy is essentially kinematic when extra-actuated joints add kinematic degrees of freedom and make the total number of degrees of freedom larger than the dimension of the task space Manuscript received April 15, 2003; revised February 15, 2004 This paper was recommended publication by Associate Editor A Maciejewski and Editor I Walker upon evaluation of the reviewers comments This work was completed during the visit of M G Mohamed to Laval University This work was supported by the Canada Research Chair Program and the Natural Sciences and Engineering Research Council of Canada (NSERC) M G Mohamed is with El-Minia University, Faculty of Engineering, Department of Production Engineering and Design, El-Minia 61111, Egypt ( m_gaber51@yahoocom) C M Gosselin is with Université Laval, Department de Génie Mécanique, Québec, Canada G1K 7P4 ( gosselin@gmculavalca) Digital Object Identifier /TRO The addition of redundancy in manipulators with closed kinematic chains has also been studied [8] [12] Moreover, the possibilities of redundancy in parallel manipulators and their effective utilization have been studied recently [13] [25] Redundancy in parallel manipulators can easily be explained in terms of mobility When the mobility of a manipulator is greater than the required degrees of freedom, the manipulator is called a kinematically redundant manipulator On the other hand, when the number of actuators is greater than the mobility, the manipulator is called redundantly actuated manipulator [19] However, most of the studies [13] [22] have focused on one type of redundancy; actuation redundancy Most recently some studies has been published on the other type of redundancy in parallel manipulators; namely kinematic redundancy [23] [27] Wang and Gosselin [24] studied the singularity of three new types of kinematically redundant parallel manipulators Mohamed in [26] introduced clear and distinct definitions of all types of redundancy in parallel manipulators and determined the degree of redundancy of every type Furthermore, Mohamed in [27] investigated the kinematics of both kinematically and actuation-redundant parallel manipulators He studied the singularity of such manipulators and specified all possible cases of their singularities Redundancy can, in general, improve the ability and permance of parallel manipulators Using the extra degrees of freedom, the redundant mechanism will not only execute the original output task but also additional tasks such as eliminating singularities, increasing the workspace, improving dexterity and obstacle avoidance, optimizing ce transmission, and/or compensating unexpected impact Apart from [25], all published researches in the area of parallel manipulator redundancy were focused on manipulators with rigid (nonconfigurable) platms and on grasping hands to be attached to the platms Conventional grippers usually are not appropriate to grasp irregular of large objects None was focused on the idea of using the platm itself as a grasping device by implementing the additional redundant degrees of freedom reconfiguring the shape of the platm itself Yi et al [25] proposed a planar parallel mechanism that has the potential of being used as a parallel-type gripper They used a parallelogrammic planar platm that can be folded Based on the platm special geometry, they tailored the kinematic analysis of their mechanism The present paper highlights the idea of using configurable platms in both planar and spatial redundant parallel manipulators, and generalizes their analysis Several new designs of possible kinematically redundant planar and spatial parallel manipulators with configurable platm are presented Such designs can be used as grasping devices especially /$ IEEE

2 278 IEEE TRANSACTIONS ON ROBOTICS, VOL 21, NO 3, JUNE 2005 There are a total of 1-DOF joints in the manipulator Only,, of them are actively controlled joints and the remaining joints are passive joints Viewing the manipulator as a network with the links being nodes and the joints being edges, the number of independent loops of the manipulator can be determined using Euler equation For symmetric parallel manipulators in which the number of links and joints in each serial-chain is the same, the total number of joints is and the total number of independent loops is The additional task of reconfiguring the platm spans an -dimensional additional space, where r is the degree of redundancy, in general The degree of redundancy r of kinematically redundant parallel manipulators can be defined as Fig 1 A general spatial kinematically redundant parallel manipulator with configurable platm irregular or large objects or even as micro-positioning devices after grasping the object Screw algebra is used to develop a general framework that can be adapted to analyze the kinematics of any general-geometry planar or spatial kinematically redundant parallel manipulator with configurable platm It can also express the twist representing the instantaneous motion of any link of the configurable platm II GENERAL MANIPULATOR GEOMETRY Fig 1 illustrates a general spatial kinematically redundant parallel manipulator with configurable platm It has a general mobility M and is moving in a space of dimension d The general or full-cycle mobility M is the number of independent variables needed to specify any configuration of the manipulator It can be determined from where is the total number of links of the manipulator, is the total number of joints, and is the DOF of joint ( ) In kinematically redundant fully parallel manipulators, there are,, limbs connecting the configurable platm to the fixed base Each limb consists of several links connected serially together by joints Since, a cylindrical joint can be replaced by a revolute joint plus a coaxial prismatic joint, and a spherical joint by three noncoplanar intersecting revolute joints, each limb can be considered as a serial-chain having m,, 1-DOF joints Theree, the configurable platm is a closed chain of mobility The geometry of the configurable platm should be selected properly according to the shape and the size of the object to be grasped All internal platm angles measured at its vertices can be determined in terms of the joint angles of the configurable platm III DESIGN OF THE MANIPULATORS A Planar Manipulator Fig 2 illustrates some designs of kinematically redundant fully parallel planar manipulators with configurable platms Despite that revolute and prismatic joints can be used in planar mechanisms, only revolute joints are illustrated in the figure ease of illustration The possible arrangements of serial-chains of planar parallel manipulators are RRR, PRR, RPR, RRP, PPR, RPP, and PRP, where the three letters indicate the succession of joints starting from the fixed link The axes of any two prismatic joints in the PPR, RPP, and PRP serial-chains should not be parallel; otherwise they will be dependent The manipulator shown in Fig 2(b) is a special case of the manipulator in Fig 2(a) Black circles in the figures represent the actuated joints It is clear that the minimum number of serial-chains in the kinematically redundant fully parallel planar manipulators with configurable platms is four Partially parallel manipulators are parallel manipulators in which more than one joint is actuated in some of the serialchains or even if the serial-chain has more joints than the dimension of the task space [28] Fig 3 illustrates some of the possible designs of kinematically redundant partially parallel planar manipulators with configurable platms that stem from the fully parallel manipulators of Fig 2 The manipulators in Fig 3(a) and (b) are special cases of Fig 2(a), the manipulators in Fig 3(c) and (d) are special cases of Fig 2(c), while the manipulators in Fig 3(e) (g) are special cases of Fig 2(d) It is clear that the minimum number of serial-chains of kinematically redundant partially parallel planar manipulators with configurable platms is two

3 MOHAMED AND GOSSELIN: KINEMATICALLY REDUNDANT PARALLEL MANIPULATORS 279 Fig 2 Planar fully parallel manipulators (a) M=4and r=1 (b) M=4 and r=1 (c) M=5and r=2 (d) M=6and r=3 B Spatial Manipulators Fig 4 illustrates some possible serial-chain arrangements to be used with kinematically redundant spatial parallel manipulators These joint-arrangements are R-RRS or equivalently RSS, RRPS or equivalently SPS, PRRS or equivalently PSS, and RPRS where the four letters indicate the succession of joints starting from the fixed base, and S stands a spherical joint The RR arrangement in Fig 4(a) (c) is equivalent to the spherical joint S since the longitudinal freedom of the spherical joint is redundant Each kinematically redundant spatial fully parallel manipulator with M general mobility will have a configurable platm which is a spatial closed-loop with M links and M 1-DOF joints The types and arrangements of these M 1-DOF joints can vary from a manipulator to another Example 2 illustrates an example of a kinematically redundant spatial fully parallel manipulator with general mobility eight Fig 5 illustrates another possible Fig 3 Planar partially parallel manipulators (a) M=4and r=1 (b) M= 4 and r=1 (c) M=5and r=2 (d) M=5and r=2 (e) M=6and r=3 (f) M=6and r=3 (g) M=6and r=3 design of a kinematically redundant partially parallel planar manipulator with configurable platms that stem from the fully parallel manipulator of Example 2 The manipulator has four RPRS serial-chains with two actuated joints in each serial-chain, namely the two joints close to the base The configurable platm consists of four links connected by four universal joints (RR) Other arrangements can be obtained A Position Analysis IV ANALYSIS OF THE MANIPULATORS The direct position analysis of parallel manipulators is, in general, difficult and no unique solution exists The complexity of finding all solutions increases, in general, with the number of DOFs of the end-effector platm A closed-m solution to

4 280 IEEE TRANSACTIONS ON ROBOTICS, VOL 21, NO 3, JUNE 2005 B Velocity Analysis Because of the generality of the screw notation and the geometric insight it provides, screw algebra is implemented in the mulation The screw representing the instant motion about or along joint j in the ith serial-chain is [29] (1) Fig 4 Spatial serial-chains (a) R-RRS, (b) RRPS, (c) PRRS, (d) RPRS, and, where is a unit vector along the direction of the ISA (instantaneous screw axis) of the jth joint in the ith serial-chain is a position vector of any point on the screw axis with respect to the screw coordinate frame is the moment of about the origin of the screw coordinate frame, and is the screw pitch; revolute joints and prismatic joints Similarly let be the screw representing the instantaneous motion about or along the ith joint of the platm closed chain Define as the rate of change along or about, and as the rate of change along or about Since kinematically redundant parallel manipulators with configurable platms consist of several closed-loops, the manipulator can be considered as a multi-closed-loop mechanism and the configurable platm be treated as an extra closed-loop The general manipulator illustrated in Fig 1 has closed-loops, only M of them are independent Writing the twist loop-closure equations a multiloop mechanism with a total of N joints will result in a set of independent equations in terms of the N joint velocities, [30] and [31] The twist representing the instantaneous motion of any link in a closed-loop relative to another link in the loop can be expressed as a linear combination of the instantaneous twists of all joints in the loop that connect the two links [29] and [32] The twist loop-closure equations can be expressed as follows: and (2) Fig 5 Spatial partially parallel manipulators their direct position analysis can be obtained utilizing algebraic elimination techniques or by installing redundant sensors Only M of these twist equations are independent In fully parallel manipulators, only one joint is actuated in each serial-chain For several design considerations, the first joint from the base in each serial-chain is actively controlled However, the basic scheme of the presented analysis does not depend on the location of the actuated joints, see Example 2

5 MOHAMED AND GOSSELIN: KINEMATICALLY REDUNDANT PARALLEL MANIPULATORS 281 Furthermore, the basic idea of the presented analysis can be used partially parallel manipulators Separating the active and passive joint velocities in the set of independent twist equations, yields The set of, equations given in (3) can be written in a compact m as follows: where the manipulator-jacobian matrices are as seen in the equation at the bottom of the page and the active- and passivevelocity vectors are (4) m as, which can be expressed in matrix The ith serial-chain passive-jacobian matrix is, where its columns are the screws associated with the passive joints in the serial-chain (3), and the ith chain passive-velocity vector is If there is more than one actuated joint in the serial-chain, ie,, (3) will include serial-chain active-jacobians, where their columns are the screws associated with the active joints in the ith serial-chain and the passive-jacobians become The manipulator passive-jacobian matrix is a nonsingular matrix, in general Theree, it is possible now to determine the velocities of all passive joints in terms of the M active joints The velocity state of any link in the manipulator or the point of contact between the ith link of the configurable platm and the grasped object can now be determined by expressing the twist representing the instantaneous motion of the link as a linear combination of the instantaneous twists of the joints leading to that link These twists represent angular or linear velocities, depending on the nature of the joint The link or the point of interest will be specified according to the assigned grasping or micro-positioning task and the grasped object It is known that the manipulator passive- and active-jacobian matrices and are geometry dependent By studying the nature of both matrices singular configurations of the manipulator can be detected When the determinant of becomes zero, the manipulator is in a singular configuration For instance, if the manipulator M actuated joints are in a configuration such that their M screws are linearly dependent, the active-jacobian matrix becomes singular, or even if the configurable platm is in a configuration such that the M screws of its M joints are linearly dependent, the passive-jacobian matrix becomes singular In all these configurations, the manipulator is in singularity (5)

6 282 IEEE TRANSACTIONS ON ROBOTICS, VOL 21, NO 3, JUNE 2005 Fig 6 A planar 4-DOF parallel manipulator The singularity of parallel manipulators with nonconfigurable platms were investigated in [27] and all possible cases were specified As mentioned earlier, redundancy can be used to avoid singularity However, since kinematically redundant parallel manipulators with configurable platm the extra degrees of freedom are used in reconfiguring the platm, the manipulator will not have the ability to avoid singularity More redundancy than the required to configure the platm can be added to the system to be able to avoid singularities 1) Example 1: Four-DOF Planar Manipulator: The manipulator illustrated in Fig 6 is a planar kinematically redundant manipulator with configurable platm It has four serial-chains and a general mobility It has a total number of joints of, only four of them are actively controlled joints An instantaneous screw coordinate frame is defined with origin that coincides with the origin O of the Cartesian reference frame and parallel to its axes Let be the coordinates of the center point of the jth joint in the ith serial-chain The coordinates of the joint centers are of the portion of the ith link of the platm as shown in Fig 7, is the rotation angle of the jth joint in the ith serial-chain, and and are the cosine and sine of the sum of angles and, respectively For the planar motion and, and, and, and The manipulator consists of five closed-loops; only four of them being independent The five twist closure-loop equations of these five loops are where and,, and, are the length of the first and the second link in the ith serial-chain, is the distance

7 MOHAMED AND GOSSELIN: KINEMATICALLY REDUNDANT PARALLEL MANIPULATORS 283 Fig 7 Link i of the configurable platm of the planar example manipulator The first four loop-closure equations can compactly be expressed as where the manipulator (12 4) active- Jacobian matrix is the (12 12) passive-jacobian matrix is as seen in the first equation at the bottom of the page, the (4 1) active-velocities vector is and the (12 1) passive-velocities vector is seen in the second equation at the bottom of the page Since the (3 2) serial-chain passive-jacobian matrices can be expressed in terms of the joint screws as the manipulator passive-jacobian becomes as expressed in the equation at the bottom of the next page Theree, the velocities of all passive joints can now be determined in terms of the active joints The twist representing the instantaneous motion of the ith link of the platm can be expressed as a linear combination

8 284 IEEE TRANSACTIONS ON ROBOTICS, VOL 21, NO 3, JUNE 2005 of the instantaneous twists of the three revolute joints in the serial-chain, see Fig 7 where the angular velocity of the ith link of the platm, and the linear velocity of a point in the ith link of the platm that is instantaneously coincides with the origin O of the reference frame The linear velocity of any point on the link depending on the grasped object and the shape of the platm can be determined easily Consider points A and B on the ith platm link such that point A is at the middle distance of and point B is a hypothetical point on the link and at a perpendicular distance as shown in Fig 7 Their coordinates are The linear velocities of points A and B are as follows: Fig 8 A spatial 8-DOF parallel manipulator It is interesting to note that the general four-link- closedchain platm, the internal platm angle at the ith vertex can be determined in terms of the joint angles as,, and theree, 2) Example 2: Eight-DOF Planar Manipulator: Fig 8 illustrates an 8-DOF spatial kinematically redundant manipulator with configurable platm and eight serial-chains It has a redundancy of degree two Fig 9 shows the kinematic design of the configurable platm It has eight revolute joints The axes of joints, and, of joints and, and of joints and are parallel The manipulator has a total of N= 56 joints, only eight of them being actively controlled joints Each serial-chain is a RRPS chain where the prismatic joint is the actively actuated joint in the serial-chain An instantaneous screw coordinate frame can be defined with origin that coincides with the origin O of the Cartesian reference frame and parallel to its axes X, Y, and Z The screws of all the joints can easily be determined It is important to note that,, and, and, and As indicated in Fig 8, the manipulator consists of nine closed loops only eight of which are independent Fig 10 shows part of the manipulator in which the screw axes of the joints in two closed-loops are illustrated in detail The twist closure equations of the eight independent closed-loops are

9 MOHAMED AND GOSSELIN: KINEMATICALLY REDUNDANT PARALLEL MANIPULATORS 285 Fig 9 The spatial 2-DOF closed-chain configurable platm These eight loop-closure equations can compactly be expressed, and the manipulator (48 8) active-jacobian matrix becomes and the (48 48) passive-jacobian matrix (see the first equation at the bottom of the page) where the ith serial-chain passive-jacobian matrix is The (8 1) active-velocity vector is and the (12 1) passive-velocity vector is as shown in the second equation at the bottom of the page Theree, the veloc-

10 286 IEEE TRANSACTIONS ON ROBOTICS, VOL 21, NO 3, JUNE 2005 Fig 10 First and second closure loops ities of all 48 passive joints can now be determined in terms of the eight active joints The twist representing the instantaneous motion of the ith link of the platm can be expressed as where the angular velocity of the ith link of the platm, and 2 the linear velocity of a point on the ith link of the platm that instantaneously coincides with the origin O of the reference frame The linear velocity of any point on the link, depending on the grasped object and the shape of the platm, can be determined easily using the relative motion concept V CONCLUSION Redundancy can improve the ability and permance of parallel manipulators Moreover, the additional redundant degrees of freedom can also be used in reconfiguring the shape of the platm and in using it as a grasping device The idea of using configurable platms in both planar and spatial redundant parallel manipulators is emphasized Several designs of possible kinematically redundant planar and spatial parallel manipulators with configurable platm are presented Such designs can be used as a grasping device especially irregular or large objects or even a micro-positioning device after grasping the object Because of the generality of the screw notation and the geometric insight it provides, screw algebra is suitable the development of a general and easy-to-understand framework studying the kinematics of any general-geometry kinematically redundant parallel manipulator with configurable platm It can also express the twist representing the instantaneous motion of any link or any point of contact between any link of the configurable platm and the grasped object REFERENCES [1] J Baillieul et al, Programming and control of kinematically redundant manipulators, in Proc 23rd IEEE Conf Decision Control, Las Vegas, NV, Dec 1984, pp [2] A A Maciejewski and C A Klein, Obstacle avoidance kinematically redundant manipulators in dynamically varying environments, Int J Robot Res, vol 4, no 3, pp , 1985 [3] N Hogan, Impedance control: An approach to manipulation, ASME J Dynamic Syst Meas Control, vol 107, pp 1 24, 1985 [4] J Baillieul, Kinematic programming alternative redundant manipulators, in Proc IEEE Int Conf Robotics and Automation, St Louis, MO, Mar 1985, pp [5] B Siciliano and J-J E Slotine, A general framework managing multiple tasks in highly redundant robotic systems, in Proc IEEE Conf Robotics and Automation, Sacramento, CA, Apr 1991, pp

11 MOHAMED AND GOSSELIN: KINEMATICALLY REDUNDANT PARALLEL MANIPULATORS 287 [6] K C Park et al, Analysis and control of redundant manipulator dynamics based on an extended operational space, Robotica, vol 19, pp , 2001 [7] J Park et al, Multiple tasks kinematics using weighted pseudo-inverse kinematically redundant manipulators, in Proc IEEE Conf Robotics and Automation, Seoul, Korea, May 2001, pp [8] Y Nakamura and M Ghodoussi, Dynamics computation of closed link robot mechanisms with nonredundant and redundant actuators, IEEE Trans Robot Autom, vol 5, no 3, pp , Jun 1989 [9] M A Nahon and J Angeles, Force optimization in redundantly actuated closed kinematic chains, in Proc IEEE Conf Robotics and Automation, Scottsdale, AZ, May 1989, pp [10] J F Gardner et al, Kinematics and control of redundantly actuated closed chains, in Proc IEEE Conf Robotics and Automation, Scottsdale, AZ, May 1989, pp [11] Y Nakamura and T Ropponen, Singularity-free parameterization and permance analysis of actuation redundancy, in IEEE Conf Robotics and Automation, Cincinnati, OH, 1990, pp [12] Y Nakamura, Advanced Robotics: Redundancy and Optimization Reading, MA: Addison-Welsey, 1991 [13] M A Nahon and J Angeles, Reducing the effect of shocks using redundant actuation, in Proc IEEE Conf Robotics and Automation, Sacramento, CA, Apr 1991, pp [14] R Kurtz and V Hayward, Multiple-goal kinematic optimization of parallel spherical mechanism with actuator redundancy, IEEE Trans Robot Autom, vol 8, no 5, pp , Oct 1992 [15] K E Zanganeh and J Angeles, Instantaneous kinematics and design of a novel redundant parallel manipulator, in Proc IEEE Conf Robotics and Automation, San Diego, CA, May 1994, pp [16], Mobility and position analysis of a novel redundant parallel manipulator, in Proc IEEE Conf Robotics and Automation, San Diego, CA, May 1994, pp [17] B Dasgupta and T S Mruthyunjaya, Force redundancy in parallel manipulators: Theoretical and practical issues, Mech Mach Theory, vol 33, no 6, pp , 1998 [18] S Kim, Operational quality analysis of parallel manipulators with actuation redundancy, in Proc IEEE Conf Robotics and Automation, Albuquerque, NM, Apr 1997, pp [19] H L Lee et al, Optimal design of a five-bar finger with redundant actuation, in Proc IEEE Conf Robotics and Automation, Leuven, Belgium, May 1998, pp [20] S Kock and W Schumacher, A parallel x-y manipulator with actuation redundancy high-speed and active-stiffness Applications, in Proc IEEE Conf Robotics and Automation, Leuven, Belgium, May 1998, pp [21], A mixed elastic and rigid-body dynamic model of an actuation redundant parallel robot with high-reduction gears, in Proc IEEE Conf Robotics and Automation, San Francisco, CA, Apr 2000, pp [22] S H Lee et al, Control of impact disturbance by redundantly actuated mechanisms, in Proc IEEE Conf Robotics and Automation, Seoul, Korea, May 2001, pp [23] G F Liu et al, Analysis and control of redundant parallel manipulators, in Proc IEEE Conf Robotics and Automation, Seoul, Korea, May 2001, pp [24] J Wang and C Gosselin, Singularity analysis and design of kinematically redundant parallel mechanisms, in Proc ASME Design Engineering Technical Conf, Montreal, QC, Canada, Sept 2002 [25] B-J Yi et al, Design of a parallel-type gripper mechanism, Int J Robot Res, vol 21, no 7, pp , 2002, to be published [26] M G Mohamed, On the redundancy of parallel manipulators, presented at the IEEE 7th Int Conf Intelligent Engineering Systems, Assiut-Luxor, Egypt, 2003 [27], Kinematic analysis of redundant parallel manipulators, presented at the IEEE 7th Int Conf Intelligent Engineering Systems, Assiut-Luxor, Egypt, 2003 [28], Structural kinematics of partially-parallel robotic mechanisms, in 1987 ASME Design Automation Conf, Boston, MA, 1987 [29], Instantaneous kinematics and joint displacement analysis of fully-parallel robotic devices, PhD dissertation, Univ Florida, Gainesville, FL, 1983 [30] F Freudenstein and R Alizade, On the degree of freedom of mechanisms with variable general constraint, in Proc 4th World Congr Theory of Machines and Mechanisms, 1975, pp [31] T H Davies, Kirchhoff circulation law applied to multiloop kinematic chains, Mech Mach Theorey, vol 16, pp , 1981 [32] M G Mohamed and J Duffy, A direct determination of the instantaneous kinematics of fully-parallel robot manipulators, ASME J Mechanisms, Transmission, Autom Design, vol 107, pp , 1983 Maher G Mohamed was born in December 1951 in El-Minia, Egypt He received the BSc degree in mechanical engineering from El-Minia University in 1974; the MSc degree from Washington State University, Pullman, in 1980; and the PhD degree from the University of Florida, Gainesville, in 1983 In 1984, he was appointed by the Department of Mechanical Engineering at El-Minia University where he has been Full Professor since 1995 He is currently the Vice President of El-Minia University In 1987, he accepted an associate professor on leave at the College of Technology, Jeddah, Kingdom of Saudi Arabia In 1995, he accepted a post-doctoral fellowship from the University of Florida, CIMAR In 2002, he spent three months at the Université Laval, Québec, QC, Canada His research interests are kinematics and dynamics of robotic mechanical systems with a particular emphasis on the parallel manipulators and complex mechanisms He is the author of the Kinematics and Dynamics of Mechanisms and Machines (Dar-Heraa, 1999) Dr Mohamed is a member of ASME, ASE, and the Egyptian National Committee of Theoretical and Applied Mechanics Clément M Gosselin (S 88 M 88) received the BEng degree in mechanical engineering from the Université de Sherbrooke, Sherbrooke, QC, Canada, in 1985, at which time he was presented with the Gold Medal of the Governor General of Canada He then received the PhD degree from McGill University, Montréal, QC, Canada His research interests are kinematics, dynamics and control of robotic mechanical systems, with a particular emphasis on the mechanics of grasping, and the kinematics and dynamics of parallel manipulators and complex mechanisms In 1988, he accepted a postdoctoral fellowship from the French government in order to pursue work at INRIA in Sophia-Antipolis, France a year In 1989 he was appointed by the Department of Mechanical Engineering at Université Laval, QC, Canada, where he has been Full Professor since 1997 He is currently a Canada Research Chair on Robotics and Mechatronics since January 2001 He also received, in 1993, the I Omega Smith award from the Canadian Society of Mechanical Engineering, creative engineering In 1995, he received a fellowship from the Alexander von Humboldt foundation which allowed him to spend six months as a Visiting Researcher in the Institut für Getriebetechnik und Maschinendynamik of the Technische Hochschule,Aachen, Germany In 1996, he spent three months at the University of Victoria, Victoria, BC, Canada, which he received a fellowship from the BC Advanced Systems Institute He is the French Language Editor the international journal Mechanism and Machine Theory Dr Gosselin received the D W Ambridge Award from McGill the best thesis of the year in Physical Sciences and Engineering in 1988 He is a member of the ASME and CCToMM