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### Editorial

J. Mechanisms Robotics. 2011;3(2):020201-020201-3. doi:10.1115/1.4003181.
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As we move into the second decade of the 21st century, we can identify three research trends that we can expect to persist into the future. They are the analysis and synthesis of (i) spatial mechanisms and robotic systems, (ii) compliant linkage systems, and (iii) tensegrity and cable-driven systems. In each case, we find that researchers are formulating and solving polynomial systems of total degrees that dwarf those associated with major kinematics problems of the previous century.

Commentary by Dr. Valentin Fuster

### Research Papers

J. Mechanisms Robotics. 2011;3(2):021001-021001-7. doi:10.1115/1.4003414.

This paper presents a novel multifingered hand with an articulated palm that makes the hand adaptable and reconfigurable. The posture of the new multifingered hand is enhanced by the additional motion of the palm and the workspace of fingers is augmented by the palm workspace. To analyze this integrated workspace, this paper introduces finger-operation planes to relate the finger motion to the palm motion and its configuration. Normals of these operation planes are used to construct a Gauss map. Adding an additional dimension, a four-dimensional ruled surface can be generated from this map to illustrate variation of posture. With the change of palm configurations, a posture manifold can be developed from the posture ruled surfaces. The workspace analysis is developed by introducing a palm workspace-triangle. This workspace-triangle evolves into a helical workspace-triangle tube when palm inputs vary and further develops into a four-dimensional presentation. This progresses into a set of workspaces of the multifingered hand by varying the palm configuration, leading to a larger workspace of the new multifingered hand as the union of the workspaces corresponding to individual palm configuration. This paper further investigates manipulability of the multifingered hand by modeling the contact point as a hypothetical spherical joint. Based on reciprocity relationship of screw systems, the finger Jacobian matrices and the hand Jacobian matrix are established. With singular value decomposition, manipulability of each finger is explored and the hand manipulability is revealed by the diagonal nature of the Jacobian matrix of the hand.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021002-021002-11. doi:10.1115/1.4003446.

This paper presents detailed design, analysis, prototyping, and testing of a novel force-reflecting hand-controller allowing physicians to control a robotic wrist and perform ultrasound examinations on patients in remote locations. The proposed device is a four degree-of-freedom mechanism with a fixed center-of-motion and uses symmetric parallel mechanisms. All movements of the device are kinematically decoupled, i.e., the hand-controller has independent drive systems for each standard ultrasound motion. A technique has been adapted to statically balance the weight of the device over its entire workspace using a single tension spring. The prototype of the device has been constructed and evaluated for ultrasound imaging of kidney and spleen. Maximum and accuracy of the output force are analytically determined and performance of the device in terms of static balancing, static-friction break-away force, and maximum achievable impedances are experimentally evaluated.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021003-021003-10. doi:10.1115/1.4003528.

This paper presents forward and inverse analyses of the response of a compliant link actuated by a discretely attached shape memory alloy (SMA) wire subjected to a time-varying input voltage. The framework for a constrained recovery of the shape memory alloy wire is developed from a robust numerical model. The model for the large deflection of a beam element due to follower forces resulting from discrete actuation using a SMA wire is coupled with the proposed framework. Thus, the response of the link is correlated with the input voltage. The algorithm for implementing this framework has been demonstrated along with some numerical examples. Experiments have also been conducted on a SMA actuated cantilever beam, and the results are compared with those of the simulations. A qualitative agreement between the two is observed. It is concluded that the theoretical results can provide a reference signal for active control of the link to achieve higher accuracy.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021004-021004-13. doi:10.1115/1.4003580.

Several systematic approaches have been developed for the optimal design of cable-based systems. Global indices are usually employed to quantify the effectiveness of a specific design inside a reference region of the workspace. The performances at the moving platform are strictly related to cable configuration, which, in turn, depends on the pose of the moving platform. As a result, traditional designs are characterized by the high variability of performances within the workspace and are often badly tailored to the design goals. The motivation behind this paper is to formalize a new design methodology for cable-driven devices. Based on a total or partial decoupling between cable disposition and end-effector pose, this methodology allows us to achieve well-tailored design solutions for a given design requirement. The resulting systems are here defined as adaptive cable-driven systems. Two simple design problems are presented and solved with both the traditional and the novel approaches, and the advantages of the latter are emphasized by comparing the resulting design solutions.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021005-021005-10. doi:10.1115/1.4003581.

A systematic approach is proposed to determine the tensionable workspace of multibody cable-driven mechanisms. The method is also capable of finding analytical descriptions for the boundaries of the tensionable regions for any number of redundant cables used. The presented approach builds upon the available methods for conventional (rigid body) cable-driven mechanisms, i.e., null space analysis and supporting/separating hyperplanes. It extends these methods to the case of a multibody driven by cables. For this purpose, the notion of generalized forces and Lagrange’s method is used to eliminate the constraint forces/moments from the equilibrium equations. This has resulted in a more compact equation form with fewer unknowns. The method is then applied to several one- and two-DOF mechanisms with various cable distributions. Analytical descriptions for the boundaries of their workspaces are found. These boundaries and the resulting regions are then used to improve the design for larger tensionable workspaces.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021006-021006-10. doi:10.1115/1.4003690.

Based on the Lie-group-algebraic properties of the displacement set, the 4DOF primitive generators of the Schoenflies motion termed $X$-motion for brevity are briefly recalled. An $X$-motion includes 3DOF spatial translation and any 1DOF rotation provided that the axes are parallel to a given direction. The serial concatenation of two generators of 4DOF $X$-motion produces a 5DOF motion called double Schoenflies motion or $X-X$-motion for brevity, which includes 3DOFs of translations and any 2DOFs of rotations if the axes are parallel to two independent vectors. This is established using the composition product of two Lie subgroups of $X$-motion. All possible 5DOF serial chains with distinct general architectures for the generation of $X-X$-motion are comprehensively introduced in the beginning. The parallel setting between a fixed base and a moving platform of two 5DOF $X-X$ limbs, under particular geometric conditions, makes up a 4DOF isoconstrained parallel generator (abbreviated as $IPG-X$) of a Schoenflies motion set. “Isoconstrained” is synonymous with “nonoverconstrianed,” and the corresponding chains are trivial chains of the 6D group of general 6DOF motions and can move in the presence of manufacturing errors. Moreover, related families of $IPG-X$s are also deducted by using the reordering or the commutation of the factor method, which yields more 5D subsets of displacements containing also the $X$-motion of the end effector. In that way, several novel general-type architectures of 4DOF parallel manipulators with potential applications are synthesized systematically in consideration of the actuated pairs near the fixed base.

Topics: Motion , Generators , Chain
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021007-021007-7. doi:10.1115/1.4003579.

With the implementation of just one mechanism, variable topology mechanisms can serve the functions of many mechanisms by changing their topology. These types of mechanisms have raised interest and attracted numerous studies in recent years, yet few of these studies have focused discussing of these mechanisms in light of their operation space. As the change of a variable topology mechanism is induced by either intrinsic constraints or constraints due to the change of joint geometry profile, the operation space of kinematic joints and kinematic chains in various working stages is changed in accordance. A theoretic framework based on the concept of the operation space of variable topology mechanisms is presented here. A number of characteristics with regard to the motion compatibility among joints and loops in different working stages are derived, laying a foundation for systematical synthesis of variable topology mechanisms. Design of a novel latch mechanism for the standardized mechanical interface system is given as an illustrative example for the synthesis of a variable topology mechanism.

Topics: Motion , Topology , Mechanisms
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021008-021008-12. doi:10.1115/1.4003272.

Trajectory tracking is accomplished by obtaining separate solutions to the geometric path-tracking problem and the temporal tracking problem. A methodology enabling the geometric tracking of a desired planar or spatial path to any order with a nonredundant manipulator is developed. In contrast to previous work, the equations are developed using one of the manipulator’s joint variables as the independent parameter in a fixed global frame rather than a configuration-dependent canonical frame. Both these features provide significant practical advantages. Furthermore, a strategy for determining joint velocities and accelerations at singular configurations is provided, which allows the manipulator to approach and/or move out of a singular configuration with finite joint velocities without sacrificing the geometric fidelity of tracking. An example shows a spatial six-revolute robot tracking a trajectory using the developed method in conjunction with resolved-acceleration feedback control.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021009-021009-8. doi:10.1115/1.4003846.

The dimensional synthesis of spatial chains for a prescribed set of positions can be applied to the design of parallel robots by joining the solutions of each serial chain at the end-effector. This design method does not provide with the knowledge about the trajectory between task positions and, in some cases, may yield a system with negative mobility. These problems can be avoided for some overconstrained but movable linkages if the finite-screw system associated with the motion of the linkage is known. The finite-screw system defining the motion of the robot is generated by a set of screws, which can be related to the set of finite task positions traditionally used in the synthesis theory. The interest of this paper lies in presenting a method to define the whole workspace of the linkage as the input task for the exact dimensional synthesis problem. This method is applied to the spatial RPRP closed linkage, for which one solution exists.

Topics: Screws , Linkages , Chain , Equations
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021010-021010-7. doi:10.1115/1.4003847.

In this paper, the author proposes a new method to design SCARA robots for higher repeatability. First, the author outlines various procedures used in optimal robot design and then points out among the various performance indices those related to repeatability. The author adds some new criteria issued from the stochastic ellipsoid theory. Another innovative part of the paper is to take into account a task-oriented strategy during the design stage, meaning the possibility of adapting task orientation and location in the robot workspace. These concepts are applied to SCARA optimal design. The method described here consists of considering simultaneously robot geometry and joint repeatability, keeping both the reach and the total cost of the sensors constant. It results in an optimization problem with adimensional ratios, which then allows easy comparisons with existing SCARA. The results are surprising and give some clues to answer the underlying question: Are industrial SCARA designed for high repeatability?

Topics: Robots , Design , Sensors
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021011-021011-8. doi:10.1115/1.4003849.

This paper presents the stiffness analysis of a planar 2DOF tensegrity mechanism. A stiffness model is first derived based on an existing formulation. Several stiffness indices having physical meaning are then extracted from the stiffness matrix for performance evaluation purposes. Stiffness mappings based on these stiffness indices are then plotted over the mechanism’s workspace and observations are made. It is shown, for instance, that in the case of the planar 2DOF tensegrity mechanism, the effect of the prestress on the stiffness is generally not significant when the stiffnesses of the cables and struts are assumed to be linear.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021012-021012-8. doi:10.1115/1.4003844.

For many single-loop closed-chain mechanisms, mobility may be characterized by the closure of sets in the theory of Lie groups. The four-revolute (4R) Bennett mechanism remains a persistent exception, requiring the formulation and expression of solutions to the loop closure relations, either directly or indirectly through spatial geometric figures. The simpler loop closure relations of the revolute-revolute-revolute-spherical (RRRS) loop, however, place conditions on the mobility of the 4R mechanism. That loop closure in turn may be interpreted as the congruence of a pair of ellipses. This new result is applied to proving the uniqueness of the Bennett mechanism along with deriving conditions where it is free from singularities. Design parameters are also identified for overconstrained RRRS mechanisms with 1DOF that are neither plane nor line symmetric. Such mechanisms, however, place the S-joint along the revolute axis of an underlying Bennett mechanism.

Topics: Mechanisms , Linkages
Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021013-021013-13. doi:10.1115/1.4003845.

This paper presents a general and systematic approach for geometric error modeling of lower mobility manipulators. The approach can be implemented in three steps: (1) development of a linear map between the pose error twist and source errors within an individual limb using the homogeneous transformation matrix method; (2) formulation of a linear map between the pose error twist and the joint error intensities of a lower mobility parallel manipulator; and (3) combination of these two models. The merit of this approach lies in that it enables the source errors affecting the compensatable and uncompensatable pose accuracy of the platform to be explicitly separated, thereby providing designers and/or field engineers with an informative guideline for the accuracy improvement achievable by suitable measures, i.e., component tolerancing in design, manufacturing and assembly processes, and kinematic calibration. Three typical and well-known parallel manipulators are taken as examples to illustrate the generality and effectiveness of this approach.

Commentary by Dr. Valentin Fuster
J. Mechanisms Robotics. 2011;3(2):021014-021014-8. doi:10.1115/1.4003848.

It is difficult to manufacture parallel manipulators (PMs) with multiple revolute joint axes intersecting at one point. These types include the 3DOF spherical parallel manipulators (SPMs), the 4DOF 3R1T and 2R2T PMs, the 5DOF 3R2T PMs, etc. PMs with this problem are hard to achieve the expected mobility. In this paper, a 3-RPS cubic PM is studied, which has three rotational freedoms and is without those intersecting axes. The motion property of this PM will not change when the manufacturing errors exist. In order to show its orientation capability, the orientation workspace of this PM is analyzed. More discussions about the differences between the traditional SPMs and this PM are proposed. The results show that compared with the traditional SPMs, this 3-RPS cubic PM can also achieve three rotational motions with an enough orientation capability for applications and it has the advantage of easy fabrication.

Commentary by Dr. Valentin Fuster

### Technical Briefs

J. Mechanisms Robotics. 2011;3(2):024501-024501-6. doi:10.1115/1.4003445.

This paper deals with the forward displacement analysis and singularity analysis of a special 2-DOF 5R spherical parallel manipulator, in which the angle between the axes of any two adjacent revolute joints is a right angle. An alternative formulation of the kinematic equations of the 5R spherical parallel manipulator is proposed. A formula is then derived to produce directly the unique current solution to the forward displacement analysis of the 5R spherical parallel manipulator. It will also be addressed to keep the spherical parallel manipulator in the same working mode and assembly mode by simply restraining the range of an input angle. Unlike other parallel manipulators, the 5R spherical parallel manipulator always undergoes self-motion in a type-II singular configuration, and the 3R leg of the 5R spherical parallel manipulator also always undergoes self-motion in a type-I singular configuration.

Commentary by Dr. Valentin Fuster