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Reactionless mechanisms have many important applications because of their zero reaction forces and moments at the base. However, in most cases, these mechanisms consume more energy than their unbalanced counterparts. This paper focuses on analyzing the relationship between the needed input torque and the dynamic parameters of reactionless four-bar linkages. The objective is to minimize the needed input torque by optimizing the relevant dynamic parameters. The dynamic analysis shows that the needed input torque mainly depends on the mass of the link, which needs to be balanced. The results obtained can be applied to the design optimization and dynamic control of the devices such as parallel manipulators composed of reactionless four-bar linkages. [DOI: 10.1115/1.4001337] Keywords: dynamic optimization, reactionless four-bar linkage, input torque

The intrinsic interaction of a robotic system that includes two 6-degree-of-freedom cable-driven platforms sharing a common workspace might result in cable interferences for random trajectories. This paper presents and analyzes computational methods for geometrically determining and managing these interferences for any trajectory constrained with variable loads. The algorithms considered determine which cable can be released from an active actuation state while allowing control in a minimal tension state, thereby ensuring that both platforms stay in a controllable workspace. The process of managing cable interferences constitutes a challenge as one must take into account the inherent limitations of the workspace, which not only include the possibility of interference itself, but also the geometry of the cable-driven locomotion interface (CDLI), its dynamics, the nonideal behavior of real cables, and the requirement that both platforms must be completely constrained at any time. As releasing a cable from an active actuation state might generate tension discontinuities in the other cables, this paper also proposes collision prediction schemes that are only applied to redundant actuators in order to reduce or completely eliminate such discontinuities. Finally, a simulation of a CDLI embedded as a peripheral in a virtual environment, in which the load applied on each platform comes from the wrench measured under the foot for a natural gait walking, is thoroughly analyzed. Index Terms--Cable, environment, interface, interference, locomotion, parallel, robot, virtual, wire.

Over the past decade, cable-driven parallel mechanisms have been used for several purposes. In this paper, a novel application is proposed, namely, using two 6DOF cable-driven parallel mechanisms sharing a common workspace to obtain the mechanical base for the design of a locomotion interface. The methodology used to develop the architecture of the mechanisms is presented, and the two main criteria used to optimize the geometry are described. These criteria are based on the wrench-closure workspace and a detection of the mechanical interferences between all the entities of the locomotion interface (cables and moving bodies). Then, the final design is described and its performances are given. Finally, in order to validate the relevance of the mechanism for the locomotion interface's design, tensile forces in the cables are computed to observe the maximal values reached during a typical human gait trajectory. [DOI: 10.1115/1.2965607] Keywords: cable-driven parallel mechanism, design optimization, locomotion interface

Byline: Marc Arsenault (Department of mechanical engineering, The Royal Military College of Canada, Kingston, Ontario, Canada K7K 7B4, marc.arsenault@rmc.ca); Clement M. Gosselin (Departement de genie mecanique, Universite Laval, Quebec, Quebec, [...]

A six-DOF wrist-partitioned parallel manipulator is a parallel manipulator in which three of the six actuated joints are used to control the position of a point on the moving platform while the other three are further used to control the orientation of the moving platform. Such parallel manipulators are, in fact, the parallel counterparts of the wrist-partitioned serial manipulators, which are widely used in industry. Unlike parallel manipulators of a general structure, a six-DOF wrist-partitioned parallel manipulator usually has simple kinematic characteristics such as its forward displacement analysis and singularity analysis are easy to solve. This paper deals with the type synthesis of six-DOF wrist-partitioned parallel manipulators. An approach is first proposed for the type synthesis of this class of parallel manipulators. Using the proposed approach, six-DOF wrist-partitioned parallel manipulators can be constructed from the types of three-DOF nonoverconstrained spherical parallel manipulators. A large number of six-DOF wrist-partitioned parallel manipulators are then obtained, and several types of practical relevance are also identified. Keywords: parallel mechanism, wrist-partioned manipulator, type synthesis

This paper presents an algorithm for the determination of singularity-free zones in the workspace of the planar 3-PRR mechanism. The mathematical derivation of the algorithm is first given. Numerical examples are then included to demonstrate the application of the proposed approach. [DOI: 10.1115/1.2717234]

There are usually several motion patterns having the same degrees of freedom (DOF). For example, planar motion, spherical motion, and spatial translation are motion patterns with 3 DOE An f-DOF parallel mechanism with multiple operation modes is a parallel mechanism that can generate different motion patterns with f DOE Up to now, no method has been proposed for the type synthesis of parallel mechanisms with multiple operation modes. This paper presents a general method for the type synthesis of parallel mechanisms with multiple operation modes. Using the proposed approach, 3-DOF parallel mechanisms with both spherical and translational modes, i.e., parallel mechanism generating both a spherical motion pattern and a spatial translational motion pattern, are generated systematically. A large number of parallel mechanisms with both spherical and translational modes are obtained. [DOI: 10.1115/1.2717228] Keywords: parallel mechanism, parallel mechanism with multiple operation modes, type synthesis, screw theory

A four-degree-of-freedom (DOF) 3T1R parallel manipulator is presented in this paper. This manipulator generates the family of so-called Schonflies motions, SCARA motions or 3T1R motions, in which the moving platform can translate in all directions and rotate around an axis of a fixed direction. The kinematic analysis of this architecture is presented, including the study of the constraint singular configurations, kinematic singular configurations, and the determination of the workspace. A prototype (the Quadrupteron) is also presented and demonstrated. The characteristics of the proposed prototype are (a) there is no constraint singularity, (b) its input-output equations are partially decoupled, (c) its kinematic singular configurations can be expressed using an equation in the angle of rotation of the moving platform and are thus easy to avoid at the design stage, and (d) its forward displacement analysis requires the solution of a univariate quadratic equation and can therefore be solved efficiently. [DOI: 10.1115/l.2717611] Keywords: parallel manipulator, Schonflies motion, 4-DOF manipulator, SCARA motion, kinematic decoupling, singularities

The computation of the equilibrium configurations of tensegrity mechanisms is often a very tedious task even for relatively simple architectures. However, it has been observed that the complexity of this problem is significantly reduced when gravitational loads are compensated with the use of static balancing techniques. In this work, the general static balancing conditions are adapted for the case of tensegrity mechanisms. Afterward, the modified conditions are applied to two new spatial three-degree-of-freedom tensegrity mechanisms. [DOI: 10.1115/1.2406100]

This paper presents a methodology for the analytical determination and representation of the workspace boundaries of symmetrical spherical parallel mechanisms (SPMs). The methodology is based on an intuitive orientation representation which, while not well known, has proven to be very useful for the analysis of symmetrical parallel mechanisms. The latter, previously introduced as "tilt-and-torsion angles," are briefly described. Then, relatively simple analytical expressions are found for the workspace boundaries of general symmetrical SPMs. Next, using these expressions and a simple numerical procedure, a fast algorithm is proposed for representing the so-called constant-torsion workspace. Finally, several examples are provided. Index Terms--Design, Euler angles, kinematics, orientation representation, singularities, spherical parallel robots, workspace.

Abstract In this paper, a methodology is proposed for the analysis of the force capabilities of connected differential mechanisms. These systems are the key elements used to extend the principle [...]

One of the drawbacks of conventional mechanisms is the significant inertia of their moving parts. Tensegrity mechanisms, which have a reduced mass because of their extensive use of cables and springs, represent a potential alternative to these mechanisms for certain types of applications. In this paper a new spatial three-degree-of-freedom tensegrity mechanism is developed and analyzed. Mathematical models of the kinematics, statics, and dynamics of the mechanism are generated. These models reveal several characteristics of the fundamental behavior of tensegrity mechanisms that make them rather unique. [DOI: 10.1115/1.2218881]

The mobile platform of a parallel cable-driven mechanism is connected in parallel to a base by lightweight links, such as cables. Since the cables can only work in tension, the set of poses of the mobile platform for which the cables can balance any external wrench, i.e., for which the platform of the mechanism is fully constrained, is often limited or even nonexistent. Thus, the study and determination of this set of poses, called the wrench-closure workspace (WCW), is an important issue for parallel cable-driven mechanisms. In this paper, the case of planar parallel cable-driven mechanisms is addressed. Theorems that characterize the poses of the WCW are proposed. Then, these theorems are used to disclose the parts of the reachable workspace which belong to the WCW. Finally, an efficient algorithm that determines the constant-orientation cross-sections of these parts is introduced. Index Terms--Cable-driven mechanisms, parallel mechanisms, workspace, wrench-closure.

This paper studies the grasp stability, of two classes of three-phalanx underactuated fingers with transmission mechanisms based on either linkages or tendons and pulleys. The concept of underactuation in robotic fingers--with fewer actuators than degrees of freedom--allows the hand to adjust itself to an irregularly shaped object without complex control strategy and sensors. With a n-phalanx finger, n contacts (one for each phalanx) are normally required to statically constrain the finger. However, some contact forces may be lacking due to either the transmission mechanism, or simply the object size and position. Thus, one may define an ith order equilibrium, when the finger is in static equilibrium with i missing contacts. In this paper, the case for which n=3 is studied with a particular emphasis on the cases for which i = 1 and i = 2. The fact that some contact forces do not appear or are negative, can lead in some cases to the ejection of the object from the hand, when no equilibrium configuration is achieved.

The determination of the 6D singularity locus of the general Gough-Stewart platform is discussed in this article. The derivation of the velocity equation and the corresponding Jacobian matrices is first presented. Then a new procedure is introduced to obtain the analytical expression of the singularity locus, which is a function of six variables (x,y,z, [phi], [theta], [psi]), using the velocity equation. Examples are also given to illustrate the results obtained. Gough-Stewart platforms can be used in several robotic applications as well as in flight simulators. The determination of the singularity locus is a very important design and application issue. [DOI: 10.1115/1.2118733]

This paper aims at developing a general framework for the use of the concept of adaptive mechanical system in the design of advanced robotic devices. The concept of adaptive mechanical system is first formalized. A design methodology is then proposed in order to formulate the associated design paradigm, based on the fundamental principles of mechanics. Finally, examples of adaptive robotic mechanical systems taken from the literature are presented in order to illustrate the application of the general design methodology.

The paper discusses forward and inverse kinematics of a class of four-degree-of-freedom (DOF), four-legged parallel mechanisms providing three rotational and one translational DOFs. A fully parametric analytical form solution to the inverse-position problem is provided. All working modes of the mechanism are shown and discussed. The equations of the forward-position problem are obtained under different leg arrangements, and a numerical example is provided. New special geometries in the class are proposed, including one suitable for keyhole surgery. Index Terms--Four-degree-of-freedom IDOF) mechanisms, kinematics, parallel mechanisms (PMs), surgical robot.

The use of tensegrity systems as structures has been extensively studied. However, their development for use as mechanisms is quite recent even though they present such advantages as reduced mass and a deployment capability. The object of this paper is to apply analysis methods usually reserved for conventional mechanisms to a planar one-degree-of-freedom tensegrity mechanism. This mechanism is obtained from a three-degree-of-freedom tensegrity system by adding actuation to the latter as well as by making some assumptions of symmetry. Analytical solutions are thus developed for the mechanism's direct and inverse static problems. Furthermore, the working curve, singularities, and stiffness of the mechanism are detailed. Finally, a dynamic model of the mechanism is developed and a preliminary control scheme is proposed.

PPR-equivalent parallel manipulators (PMs) are a class of 3-DOF PMs with great application potential. They are indeed the parallel counterparts of the 3-DOF PPR serial robots, in which the moving platform can rotate arbitrarily about an axis undergoing a planar translation. This paper deals with the type synthesis of 3-DOF PPR-equivalent PMs. At first, virtual chains are introduced to represent the motion patterns of 3-DOF motions and relevant results from screw theory are recalled. A method is then proposed for the type synthesis of 3-DOF PPR-equivalent PMs. Using the proposed approach, the type synthesis of 3-DOF PPR-equivalent PMs is performed in three steps. In addition to all the 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs proposed in the literature, a number of new 3-DOF PPR-equivalent parallel kinematic chains and 3-DOF PPR-equivalent PMs are identified. It is also found that there are no PPR-equivalent PMs with identical type of legs. The type synthesis of PPR-equivalent PMs is well solved using the proposed approach. The characteristic of the proposed approach is that the type synthesis of PPR-equivalent parallel kinematic chains is reduced to the type synthesis of 3-DOF single-loop kinematic chains and thus easy to perform.

In this paper, the design of reactionless 3-degree-of-freedom (DOF) and 6-DOF parallel manipulators is presented. At first, the design and dynamic balancing of a novel 3-DOF parallel mechanism referred to as the parallelepiped mechanism are addressed. Two types of actuation schemes of the mechanism are considered, and the two corresponding mechanical structures are designed. The balancing equations are derived by imposing that the center of mass of the mechanism is fixed and that the total angular momentum is constant with respect to a fixed point. Optimization is performed to determine the counterweights and counter-rotations based on the balancing conditions. Numerical examples of reactionless 3-DOF parallelepiped mechanisms are given. The dynamic simulation software ADAMS is used to simulate the motion of the mechanisms and to verify that the mechanisms are reactionless at all times and for arbitrary trajectories. Finally, the 3-DOF parallelepiped mechanisms are used as legs to synthesize reactionless 6-DOF parallel manipulators. Index Terms--Dynamic balancing, parallel mechanisms, parallelepiped mechanisms, reactionless.

Redundancy can, in general, improve the ability and performance 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) platforms and on grasping hands to be attached to the platforms. Conventional grippers usually are not appropriate to grasp irregular or large objects. Very few studies focused on the idea of using a configurable platform as a grasping device. This paper highlights the idea of using configurable platforms in both planar and spatial redundant parallel manipulators, and generalizes their analysis. The configurable platform 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 platform itself. Several designs of kinematically redundant planar and spatial parallel manipulators with configurable platform are presented. Such designs can be used as a grasping device especially for 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 platform. Index Terms--Analysis, configurable platform, design, kinematic redundancy, parallel manipulator.

In this paper, we present a general and systematic analysis of cable-driven planar parallel mechanisms. The equations for the velocities are derived, and the forces in the cables are obtained by the principle of virtual work. Then, a detailed analysis of the workspace is performed and an analytical method for the determination of the boundaries of an x-y two-dimensional subset is proposed. The new notion of dynamic workspace is defined, as its shape depends on the accelerations of the end-effector. We demonstrate that any subset of the workspace can be considered as a combination of three-cable subworkspaces, with boundaries being of two kinds: two-cable equilibrium loci and three-cable singularity loci. By using a parametric representation, we see that for the x-y workspace of a simple no-spring mechanism, the two-cable equilibrium loci represent a hyperbolic section, degenerating, in some particular cases, to one or two linear segments. Examples of such loci are presented. We use quadratic programming to choose which sections of the curves constitute the boundaries of the workspace for any particular dynamic state. A detailed example of workspace determination is included for a six-cable mechanism. [DOI: 10.1115/1.1830045]

This paper addresses the dynamic balancing of a planar three-degree-of-freedom parallel mechanism. A mechanism is said to be dynamically balanced if, for any motion of the mechanism, the reaction forces and torques at the base are identically equal to zero, at all times. The proposed mechanism is based on legs consisting of five-bar parallelogram linkages. The balancing equations are first obtained. Then, optimization is used in order to minimize the mass and inertia of the moving links. Finally, a numerical verification of the dynamic balancing is provided and the prototype is presented. [DOI: 10.1115/1.1798211]

In this paper, an NC interpolation algorithm for a tripod-based parallel kinematic machine is investigated. The algorithm can be implemented in two steps, the rough interpolation in the Cartesian space and the precise interpolation in the actuator space. The upper hound of the theoretical interpolation error due to the interpolation algorithm in the precise interpolation and nonlinear mapping is analyzed. The representation of the interpolation error distribution within the Cartesian space is depicted in terms of the variations of the interpolation period and the programming velocity. It was concluded that this error is sufficiently small and may be neglected. [DOI: 10.1115/1.1767184]

This paper deals with the conceptual design and optimal dimensional synthesis of a novel 2-DOF translational parallel robot for pick-and-place operations. In a conceptual design phase, the conditions for generating such kinds of parallel robots are investigated, leading to the invention of a 2-D version of the Delta robot. Combining this robot with a 1-DOF feed mechanism, a hybrid robot can be created which is particularly suitable for transporting objects at very high speed in a plane plus a relatively slow or step-by-step, yet long distance motion, normal to the plane. The kinematic optimality of the 2-DOF translational parallel robot is achieved by minimizing a global and comprehensive conditioning index subject to a set of appropriate constraints. The application of this robot to the development of a device for quality inspection of rechargeable batteries is used to demonstrate its applicability.

The aim of this paper is to establish a fundamental basis for the analysis of underactuated fingers with a general approach. A new method to obtain the force capabilities of any underactuated fingers will be presented. Force capability is defined as the ability to generate an external wrench onto a fixed object with a given set of phalanges. This method is based on the introduction of two new matrices which completely describe the relationship between the input torque of the finger actuator(s) and the contact forces on the phalanges. Using this tool, one can study the conditions under which certain phalanx forces vanish, and compare different underactuation mechanisms with a rigorous approach. Index Terms--Robot hand, shape adaptation, stable grasp, underactuation.

A reactionless mechanism is one which does not exert any reaction force or moment on its base at all times, for arbitrary trajectories of the mechanism. This paper addresses the synthesis and design of planar and spatial reactionless three-degree-of-freedom (DOF) mechanisms using four-bar linkages without separate counter-rotations. Based on the conditions of dynamic balancing of single planar four-bar linkages developed previously, the suitable architecture and parameters are first determined, and an optimized four-bar mechanism is then designed and prototyped. Planar and spatial 3-DOF reactionless mechanisms are synthesized using the reactionless four-bar linkages. The optimization of the 2-DOF mechanism as the basis mechanism of 3-DOF mechanisms is performed in order to reduce the mass of the mechanism for a given platform. Prototypes of the reactionless planar and spatial mechanisms are designed. With the help of a dynamic simulation software, it is shown that the mechanisms are reactionless for arbitrary trajectories. Index Terms--Dynamic balancing, four-bar linkages, free-floating mechanisms, parallel mechanisms (PMs), reactionless.

3T1R four-degrees-of-freedom (DOF) parallel manipulators (3T1R-PMs) are the parallel counterparts of the 4-DOF SCARA serial robots. In a 3T1R-PM, the moving platform can generate 3T1R motion (also called Schonflies motion), which refers to a rotation about any axis with a given direction in conjunction with 3-DOF translations. A method is proposed for the type synthesis of 3T1R-PMs based on screw theory. The wrench systems of a 3T1R parallel kinematic chain (3T1R-PKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of 3T1R-PMs. The type synthesis of legs for 3T1R-PKCs, the type synthesis of 3T1R-PKCs, as well as the selection of actuated joints of 3T1R-PMs, are dealt with in sequence. 3T1R-PKCs with and without inactive joints are synthesized. The phenomenon of dependent joint groups in a 3T1R-PKC is revealed for the first time. Several 3T1R-PMs with identical type of legs are obtained. Index Terms--Dependent joint group, inactive joint, screw theory, 3T1R parallel manipulator (3T1R-PM), type synthesis.

In this paper, the singularity loci of a special class of spherical 3-DOF parallel manipulators with prismatic actuators are studied. Concise analytical expressions describing the singularity loci are obtained in the joint and in the Cartesian spaces by using the expression of the determinant of the Jacobian matrix and the inverse kinematics of the manipulators. It is well known that there exist three different types of singularities for parallel manipulators, each having a different physical interpretation. In general, the singularity of type II is located inside the Cartesian workspace and leads to the instability of the end-effector. Therefore, it is important to be able to identify the configurations associated with this type of singularity and to find their locus in the space of all configurations. For the class of manipulators studied here, the six general cases and the five special cases of singularities are discussed. It is shown that the singularity loci in the Cartesian space (defined by the three Euler angles) are six independent planes. In the joint space (defined by the length of the three input links), the singularity loci are quadric surfaces, such as hyperboloid, sphere or a degenerated line or a degenerated circle. In addition, the three-dimensional graphical representations of the singular configurations in each of the general and special cases are illustrated. The description of the singular configurations provided here has great significance for robot trajectory planning and control. [DOI: 10.1115/1.1649970]

A method is proposed for the type synthesis of 3-DOF (degree-of-freedom) translational parallel manipulators (TPMs) based on screw theory. The wrench systems of a translational parallel kinematic chain (TPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of TPMs. The type synthesis of legs for TPKCs, the type synthesis of TPKCs as well as the selection of actuated joints of TPMs are dealt with in sequence. An approach to derive the full-cycle mobility conditions for legs for TPKCs is proposed based on screw theory and the displacement analysis of serial kinematic chains undergoing small joint motions. In addition to the TPKCs proposed in the literature, TPKCs with inactive joints are synthesized. The phenomenon of dependent joint groups in a TPKC is revealed systematically. The validity condition of actuated joints of TPMs is also proposed. Finally, linear TPMs, which are TPMs whose forward displacement analysis can be performed by solving a set of linear equations, are also revealed. [DOI: 10.1115/1.1637662]

This paper addresses the singularity analysis and the design of three new types of kinematically redundant parallel mechanisms, i.e., the four-degree-of-freedom planar and spherical parallel mechanisms and the seven-degree-of-freedom spatial Stewart platform. The main idea in the design of these parallel manipulators is the addition of one redundant degree of freedom in one of the kinematic chains of the nonredundant manipulator Such manipulators can be used to avoid the singularities inside the workspace of non-redundant manipulators. After describing the geometry of the manipulators, the velocity equations are derived and the expressions for the Jacobian matrices are obtained. Then, the singularity conditions are discussed. Finally, the expressions of the singularity loci of the kinematically redundant mechanisms are obtained and the singularity loci of the nonredundant and redundant manipulators are compared. It is shown here that the conditions for the singularity of the redundant manipulators are reduced drastically relative to the nonredundant ones. As a result, the proposed kinematically redundant parallel manipulators may be of great interest in several applications. [DOI: 10.1115/1.1641189]

A spherical parallel manipulator (SPM) refers to a 3-DOF (degree-of-freedom) parallel manipulator generating 3-DOF spherical motion. A method is proposed for the type synthesis of SPMs based on screw theory. The wrench systems of a spherical parallel kinematic chain (SPKC) and its legs are first analyzed. A general procedure is then proposed for the type synthesis of SPMs. The type synthesis of legs for SPKCs, the type synthesis of SPKCs, as well as the selection of inputs of SPMs are dealt with in sequence. An input validity condition of SPMs is proposed. SPKCs with and without inactive joints are synthesized. The number of overconstraints of each SPKC is also given. The phenomenon of dependent joint groups in an SPKC is revealed for the first time. [DOI: 10.1115/1.1637655] Keywords: Spherical Parallel Manipulator, Type Synthesis, Screw Theory, Inactive Joint, Dependent Joint Group

A new class of six-degree-of-freedom (DOFs) spatial parallel platform mechanism is considered in this paper. The architecture consists of a mobile platform connected to the base by three identical kinematic chains using five-bar linkages. Recent investigations showed that parallel mechanisms with such a topology for the legs can be efficiently statically balanced using only light elastic elements. This paper follows up with a workspace analysis and optimization of the design of that parallel mechanism. More specifically, considering a possible industrial application of the architecture as a positioning and orienting device of heavy loads, an optimization procedure for the maximization of the volume of the three-dimensional (3-D) constant-orientation workspace of the mechanism is first presented. As the mechanism could also have great potential as a motion base for flight simulators, we develop here a discretization method for the computation and graphical representation of a new workspace with coupled translational and rotational DOFs. This workspace can be defined as the 3-D space which can be obtained when generalized coordinates x, y and torsion angle [psi] in the tilt-and-torsion angles parametrization are constant. A second procedure is then presented for the maximization of the volume of this second subset of the complete workspace. For both approaches, our purpose is to attempt an optimal design of the mechanism by maximizing the volume of the associated 3-D Cartesian region that is free of critical singularity loci. Index Terms--Design, optimization, parallel manipulator, singularity-free workspace.

This paper presents the results of a detailed study of the singular configurations of 3-DOF planar parallel mechanisms with three identical legs. Only prismatic and revolute joints are considered. From the point of view of singularity analysis, there are ten different architectures. All of them are examined in a compact and systematic manner using planar screw theory. The nature of each possible singular configuration is discussed and the singularity loci for a constant orientation of the mobile platform are obtained. For some architectures, simplified designs with easy to determine singularities are identified. [DOI: 10.1115/1.1582878]

Selecting a mechanism for a machine tool that will best suit the needs of a forecast set of rigidities can be a difficult and costly exercise. This problem can now be addressed using a kinetostatic modeling method. In this paper, a kinetostatic model for the Tricept machine tool family is established based on lumped flexibilities. This model can be used to analyze the effect of link flexibility on the machine tool's global stiffness and the platform positioning precision. The Tricept machine tool is a new type of parallel mechanism with prismatic actuators whose degree of freedom is dependent on a passive constraining leg connecting the base and the platform. The geometric model and the mechanical design of the Tricept machine tool is first recalled. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances. It is shown that the link flexibility has a significant effect on the machine tool's precision and that it is necessary to take the link flexibility into account. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, the optimization of the stiffness is addressed using a genetic algorithm. [DOI: 10.1115/1.1471529]

Analytic manipulators are manipulators for which a characteristic polynomial of fourth degree or lower can be obtained symbolically. Six types of RPR-PR-RPR analytic planar parallel manipulators (APPMs) are first generated using the component approach and the method based on the structure of the univariate equation. Of the six types, four are composed of Assur II kinematic chains while the other two are composed of Assur III kinematic chains. The forward displacement analysis (FDA) of two types of RPR-PR-RPR APPMs composed of Assur III kinematic chains is then performed. The FDA of each of the two types of APPMs composed of Assur III kinematic chains is reduced to the solution of a univariate cubic equation and a quadratic equation in sequence. It is also proven that the maximum number of real solutions to the FDA is 4 for the RPR-PR-RPR planar parallel manipulator with one aligned platform and one orthogonal platform. Examples with 4 real solutions for the RPR-PR-RPR planar parallel manipulator with one aligned platform and one orthogonal platform or 6 real solutions for the RPR-PR-RPR planar parallel manipulator with two aligned platforms are given at the end of this paper. [DOI: 10.1115/1.1468224]

This paper presents a new type of haptic device using spherical geometry. The basic idea of haptic devices is to provide users with feedback information on the motion and/or force that he or she generates. Haptic devices have several potential applications such as, for example, fine compliant assembly, VR environment simulation, and high-precision teleoperation, especially in hazardous or hostile areas. The particular architecture of the spherical haptic device developed here will be presented and its advantages will be highlighted. Then, its basic kinematic properties, which shall be used for control and geometric optimization purposes, will be reviewed. The design optimization itself will then highlight some important features of the mechanism. The control scheme and real-time force feedback issues will then be presented. Finally, the results obtained with the prototype will be discussed. Index Terms--Design optimization, force control, haptic device, parallel mechanism, spherical mechanism.

This paper looks at the control of mechanical impedance of the so-called Gough-Stewart class of parallel platforms. Two methods of compliance control are presented. One is based on global potential energy functions that have previously been applied to controlling serial manipulators and electrodynamically levitated platforms. The second uses the exponential map to associate finite displacements of the platform from equilibrium with twist displacements. Compliant wrenches are then proportional to the twist displacements. Control of spatial damping is addressed as well, justifying the classification as impedance control. Control algorithms and simulation results are given. Index Terms - Gough-Stewart platform, impedance control, nonlinear systems, parallel robots, spatial geometry.

A new method for the determination of the workspace of complex planar robotic manipulators is described in this paper. The method is based on the use of joint limits to obtain equations describing limiting curves. These limiting curves are then segmented at their mutual intersections and validated. The resulting sets of portions of curves form the envelope of the workspace. The algorithm is completely general and can be applied to any three-degree-of-freedom planar manipulator - serial, parallel or hybrid - with or without joint limits. Examples of the application of the method to a serial three-degree-of-freedom manipulator, to a hybrid three-degree-of-freedom manipulator and to a parallel three-degree-of-freedom manipulator are given.

Relatively little research has been conducted in the field of reduced-degree-of-freedom flight simulators or in the assessment of the quality of motion sensors that might be produced in these machines. The possibilities of a variety of three-degree-of-freedom motion platforms or bases for the simulation of large transport aircraft motions are studied. Results suggest that three-degree-of-freedom simulators can produce a simulation quality that can match that produced by the six-degree-freedom Stewart platform in most cases.

An algorithm for kinematic design determines the workspace of parallel robotic manipulators with a small workspace area and planar three-degree-of-freedom. The algorithm accounts for the possible physical limitations on actuated and passive joints. The workspace area is computable at low cost with the Gauss Divergence Theorem. The algorithm is used in Computer-Aided-Design for analysis and simulation in kinematic design. Graphical representation of the workspace in 2D and 3D can be obtained.

This paper presents a new approach for the computation of generalized positioning inverse kinematic functions for Puma manipulators. This new approach leads to real solutions of the joint variables for any set of Cartesian coordinates located inside or outside the robot's workspace. Therefore, the inverse kinematic functions derived are termed 'generalized inverse kinematic functions'. These solutions, which produce the minimum distance between the end effector and a Cartesian point to be reached, are particularly useful in tracking operations. Because of the special architecture of the Puma, closed-form solutions are obtained. This leads to simple algorithms and allows for the computation of all solutions.

A method to predict the trajectory of moving objects in a robotic environment in real-time is proposed and evaluated. The position, velocity, and acceleration of the object are estimated by several neural networks using the six most recent measurements of the object coordinates as inputs. The architecture of the neural nets and the training algorithm are presented and discussed. Simulation results obtained for both 2D and 3D cases are presented to illustrate the performance of the prediction algorithm. Real-time implementation of the neural networks is considered. Finally, the potential of the proposed trajectory prediction method in various applications is discussed.

The paper proposes an approach to obtain inverse kinematic functions whose domain is not limited to the manipulator's workspace. As a result, these functions can be used to map points of the Cartesian space that do not belong to the manipulator's workspace. The positioning problem is formulated as a minimization of the distance between the prescribed Cartesian point and the end-effector. Hence, points outside the workspace of the manipulator are mapped by the inverse kinematic function into joint coordinates that bring the manipulator as close as possible to the prescribed Cartesian location. The formulation is derived for both planar and spatial motion and an extension to problems where the orientation has to be considered is also given. Examples pertaining to 2-DOF and 3-DOF manipulators are solved and both analytical and numerical results are given. The proposed inverse kinematic functions are of great interest for tracking, approach and catching operations where the object to be reached or tracked by the manipulator can be outside of the workspace.

A method for analyzing the singularities of serial manipulators is presented. The method uses analytical expressions of the Jacobian matrix to determine easily the locus of singular configurations in the manipulator's Cartesian workspace. Experiments are conducted wherein the reliability of this new method is demonstrated. Results show that the singularities lead to a locusdescribed by a hyperbola which degenerates into a straight line for some specific orientations.

Proposed dexterity indices for planar and spatial manipulators are based on specific Jacobian matrices which are invariant to the manipulator's scaling. The method considers the nd effector velocity as that of only some points on it and uses only one point's velocity with the angular velocity. Results show that the indices remain invariant under the scaling even with the position and orientation considered, providing a useful tool for kinematic optimization.