A cuspidal serial robot can travel from one inverse kinematic solution to another without crossing a singularity. Cuspidal robots ask for extra care and caution in trajectory planning, as identifying an aspect related to one unique inverse kinematic solution is not possible. The issues related to motion planning with cuspidal robots are related to the inherent property arising from the geometric design of the robot. The cuspidality property has not been considered in recent industrial 6R robots with a non-spherical wrist. In this work, cuspidality is illustrated with the JACO robot (gen 2, non-spherical wrist), a serial arm by Kinova Robotics which is deployed in various applications and is cuspidal in nature. A nonsingular change of solutions for the robot is provided to highlight the effect of cuspidal robots on the interference with the environment. The pose with multiple inverse kinematic solutions in an aspect is presented. Problems in choosing the initial solution of the path in cuspidal robots, and its consequence, is illustrated with an example path in the workspace of the JACO robot. The paper presents the importance of cuspidality analysis of 6R robots and the implications of neglecting it.

The kinematics of cuspidal 3R regional robots was studied extensively in the past. Moreover, certain industrial 6R robots were found to be cuspidal (e.g. Fanuc CRX series, Kinova GEN2), which makes cuspidal robots finally interesting for practical applications. This necessitates optimal trajectory planning, respecting the dynamics and technical limits of the particular robot. In this paper, a method for singularity-free time-optimal point-to-point trajectory (PtP) trajectory planning is proposed. As a special case, this method is applicable to time-optimal singularity-free assembly mode changing. Results are shown for 3R robots and a 6R Fanuc CRX10iA/L.

Cuspidal robots are robots with at least two inverse kinematic solutions that can be connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been studied in the past, but extending the study to six-degree-of-freedom robots can be a challenging problem. Many robots can be modeled as a polynomial map together with a real algebraic set so that the notion of cuspidality can be extended to these data.

This paper proposes a new kind of light-weight manipulators suitable for safe interactions. The proposed manipulators use anti-parallelogram joints in series, referred to as X-joints. Each X-joint is remotely actuated with cables and springs in parallel, thus realizing a tensegrity one-degree-of-freedom mechanism. As compared to manipulators built with simple revolute joints in series, manipulators with tensegrity X-joint offer a number of advantages, such as an intrinsic stability, variable stiffness and lower inertia. This new design was inspired by the musculosleketon architecture of the bird neck that is known to have remarkable features such as a high dexterity. The paper analyzes in detail the kinetostatics of a X-joint and proposes a 3-degree-of-freedom manipulator made of three such joints in series. Both simulation results and experiment results conducted on a test-bed prototype are presented and discussed.

This paper presents the preliminary studies dedicated to the design of cable-driven parallel robots (CDPRs) for industrial purposes. The goal is to transport the proper tools around a jacket, an offshore structure supporting a wind turbine, in order to perform painting and sandblasting tasks. In this paper, a simplified case study consisting of a structure composed of four tubes is investigated. A fully constrained CDPR and a suspended CDPR are studied. The design problems of the CDPRs at hand are formulated as optimization problems. They aim at determining the locations of the base anchor points of the cables that minimize the size of the CDPR, while satisfying a set of constraints. Those constraints guarantee that the moving platform can support the external wrenches and that there is no interference between the cables and between the cables and the environment, all along the path to be followed by the moving platform.

Parallel robots admit generally several solutions to the direct kinematics problem. The aspects are associated with the maximal singularity free domains without any singular configurations. Inside these regions, some trajectories are possible between two solutions of the direct kinematic problem without meeting any type of singularity: non-singular assembly mode trajectories. An established condition for such trajectories is to have cusp points inside the joint space that must be encircled. This paper presents an approach based on the notion of uniqueness domains to explain this behaviour.

Two-dimensional slices of robot singularity loci contain, in general, cusps. This kind of points are important because their presence indicates the possibility of planning assembly-changing motions that do not meet any singularity. The critical points where the number of cusps changes, as the slice is swept, permit one to decompose a singularity locus into domains where the obtained slices share common topological properties. In this paper, it is shown how Catastrophe Theory provides a solid framework to classify these critical points up to certain types of equivalence giving precise local models to describe them. It is also shown how only three possible types of these critical points exist for generic robots. The presented results are exemplified on a serial 3R robot.

We study in this paper a class of 3-RPR manipulators for which the direct kinematic problem (DKP) is split into a cubic problem followed by a quadratic one. These manipulators are geometrically characterized by the fact that the moving triangle is the image of the base triangle by an indirect isometry. We introduce a specific coordinate system adapted to this geometric feature and which is also well adapted to the splitting of the DKP. This allows us to obtain easily precise descriptions of the singularities and of the cusp edges. These latter second order singularities are important for nonsingular assembly mode changing. We show how to sort assembly modes and use this sorting for motion planning in the joint space.

In this paper, 3-PPR planar parallel manipulators with D- or U-shape base are compared with respect to their workspace size and kinematic sensitivity to joint clearances. First, the singularities and workspace of a general 3-PPR planar parallel manipulator are analyzed. Then, an error prediction model applicable to both serial and parallel manipulators is developed. As a result, two nonconvex quadratically constrained quadratic programs are formulated in order to find the maximum reference-point position error and the maximum orientation error of the moving-platform for given joint clearances. Finally, the contributions of the paper are highlighted by means of a comparative study of two manipulators.

This paper introduces a methodology to analyze geometrically the singularities of manipulators, of which legs apply both actuation forces and constraint moments to their moving platform. Lower mobility parallel manipulators and parallel manipulators, of which some legs have no spherical joint, are such manipulators. The geometric conditions associated with the dependency of six PlUumlcker vectors of finite lines or lines at infinity constituting the rows of the inverse Jacobian matrix are formulated using Grassmann-Cayley algebra (GCA). Accordingly, the singularity conditions are obtained in vector form. This study is illustrated with the singularity analysis of four manipulators.

The paper presents a new stiffness modelling method for overconstrained parallel manipulators, which is applied to 3-d.o.f. translational mechanisms. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-d.o.f. virtual springs. In contrast to other works, the method includes a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations, which allows computing the stiffness matrix for the overconstrained architectures and for the singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators.

The Orthoglide is a Delta-type PKM dedicated to 3-axis rapid machining applications that was originally developed at IRCCyN in 2000-2001 to meet the advantages of both serial 3-axis machines (regular workspace and homogeneous performances) and parallel kinematic architectures (good dynamic performances and stiffness). This machine has three fixed parallel linear joints that are mounted orthogonally. The geometric parameters of the Orthoglide were defined as function of the size of a prescribed cubic Cartesian workspace that is free of singularities and internal collision. The interesting features of the Orthoglide are a regular Cartesian workspace shape, uniform performances in all directions and good compactness. In this paper, a new method is proposed to analyze the stiffness of overconstrained Delta-type manipulators, such as the Orthoglide. The Orthoglide is then benchmarked according to geometric, kinematic and stiffness criteria: workspace to footprint ratio, velocity and force transmission factors, sensitivity to geometric errors, torsional stiffness and translational stiffness.

This paper deals with the in-depth kinematic analysis of a special parallel wrist, called the agile eye. The agile eye is a three-legged spherical parallel robot with revolute joints, in which all pairs of adjacent joint axes are orthogonal. Its most peculiar feature, demonstrated in this paper for the first time, is that its workspace is unlimited and flawed only by six singularity curves (instead of surfaces). These curves correspond to self-motions of the mobile platform and of the legs, or to a lockup configuration. This paper also demonstrates that the four solutions to the direct kinematics of the agile eye (assembly modes) have a simple direct relationship with the eight solutions to the inverse kinematics (working modes)

This paper investigates the singular curves in two-dimensional slices of the joint space of a family of planar parallel manipulators. It focuses on special points, referred to as cusp points, which may appear on these curves. Cusp points play an important role in the kinematic behavior of parallel manipulators since they make possible a nonsingular change of assembly mode. The purpose of this study is twofold. First, it reviews an important previous work, which, to the authors' knowledge, has never been exploited yet. Second, it determines the cusp points in any two-dimensional slice of the joint space. First results show that the number of cusp points may vary from zero to eight. This work finds applications in both design and trajectory planning

The design of a spherical wrist with parallel architecture is the object of this article. This study is part of a larger project, which aims to design and to build an eel robot for inspection of immersed piping. The kinematic analysis of the mechanism is presented first to characterize the singular configurations as well as the isotropic configurations. We add the design constraints related to the application, such as (i) the compactness of the mechanism, (ii) the symmetry of the elements in order to ensure static and dynamic balance and (iii) the possibility of the mechanism to fill the elliptic form of the ell sections.

A classification of a family of 3-revolute (3R) positioning manipulators is established. This classification is based on the topology of their workspace. The workspace is characterized in a half-cross section by the singular curves. The workspace topology is defined by the number of cusps and nodes that appear on these singular curves. The design parameters space is shown to be divided into nine domains of distinct workspace topologies, in which all manipulators have similar global kinematic properties. Each separating surface is given as an explicit expression in the DH-parameters.

This paper addresses the kinematics of cuspidal manipulators, i.e., nonredundant manipulators which can change posture without meeting a singularity. It focuses on the uniqueness domains and on the regions of feasible paths in the workspace. For cuspidal manipulators, the uniqueness domains are not the singularity-free regions of the joint space. It is shown that additional surfaces, called characteristic surfaces, separate the inverse kinematic solutions in the joint space. The uniqueness domains define the regions of feasible paths in the workspace. Joint limits are taken into account in this paper. This paper should help the reader better understand the kinematics of cuspidal manipulators.

The subject of this paper is the design of a new concept of modular parallel mechanisms for three, four or five-axis machining applications. Most parallel mechanisms are designed for three- or six-axis machining applications. In the last case, the position and the orientation of the tool are coupled and the shape of the workspace is complex. The aim of this paper is to use a simple parallel mechanism with two-degree-of-freedom (dof) for translation motions and to add one or two legs to add one or two-dofs for rotation motions. The kinematics and singular configurations are studied for each mechanism.

This paper addresses the architecture optimization of a three-degree-of-freedom translational parallel mechanism designed for machining applications. The design optimization is conducted on the basis of a prescribed Cartesian workspace with prescribed kinetostatic performances. The resulting machine, the Orthoglide, features three fixed parallel linear joints which are mounted orthogonally, and a mobile platform which moves in the Cartesian x-y-z space with fixed orientation. The interesting features of the Orthoglide are a regular Cartesian workspace shape, uniform performances in all directions, and good compactness. A small-scale prototype of the Orthoglide under development is presented at the end of this paper.

The aim of this paper is to characterize the notion of aspects in the workspace and in the joint space for parallel manipulators. In opposite to the serial manipulators, the parallel manipulators can admit not only multiple inverse kinematic solutions, but also multiple direct kinematic solutions. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. The study of these matrices allow one to define the parallel and the serial singularities respectively. The notion of working modes is introduced to separate inverse kinematic solutions. Thus we can find out the domains of the workspace and the joint space which exempt of singularity. An application of this study is the movability analysis in the workspace of the manipulator as well as the path-planning and control. This study is illustrated with a RR-RRR planar parallel manipulator.

The subject of this paper is a special class of closed chain manipulators. First, we analyze a family of two-degree-of-freedom (DOF) five-bar planar linkages. Two Jacobian matrices appear in the kinematic relations between the joint-rate and the Cartesian-velocity vectors, which are called the "inverse kinematics" and the "direct kinematics" matrices. It is shown that the loci of points of the workspace where the condition number of the direct-kinematics matrix remains constant, i.e., the isoconditioning loci, are the coupler points of the four-bar linkage obtained upon locking the middle joint of the linkage. Furthermore, if the line of centers of the two activated revolutes is used as the axis of a third actuated revolute, then a 3-DOF hybrid manipulator is obtained. The isoconditioning loci of this manipulator are surfaces of revolution generated by the isoconditioning curves of the 2-DOF manipulator, whose axis of symmetry is that of the third actuated revolute.

A cuspidal manipulator is one which can change posture without meeting a singularity. The non-singular posture changing ability is an important feature which should be considered when designing new manipulators. The aim of this work is to provide aids for the designer in order that, in the synthesis process, he/she has the possibility to adjust the kinematic parameters according to whether a cuspidal manipulator design is desired or not. This study applies for non-redundant 3R positioning manipulators or 6R spatial manipulators with spherical wrist.

The primary goal of this paper is a descriptive explanation, based on typical illustrative examples, of what happens precisely when a serial non-redundant manipulator is changing its posture. This work focuses on the cuspidal robot manipulators, i.e. those robot manipulators which can change posture without meeting a singularity. The analysis is done for 3-DOF positioning manipulators. It applies to 6-DOF manipulators with wrists as well. Main applications of this study are robot design and trajectory planning.

The author presents a novel general formalism for analyzing the kinematics of robot manipulators with arbitrary nonredundant geometry. It is shown that the classical description of singularities in the joint space may become insufficient. The notion of characteristic surfaces which define a new partition of the joint space is introduced. Generalizing the motion of aspects and c-sheets, the characteristic surfaces permit characterization of the joint space uniqueness domains, in which there is one unique solution to the inverse kinematic problem. The mapping into the workspace of the uniqueness domains defines the regions of feasible continuous trajectories.>

The authors describe a general method of designing and positioning a robot in an environment in order to solve geometrical problems related to the accessibility of given zones. The approach is characterized by the use of two different types of representation of the solids and of the spaces: a CSG (constructive solid geometry) and an octree representation. Each is well adapted to solve two different problems: collision detection and description of the attained space. In addition, an automatic algorithm is used to design any robot related to any set of Denavit-Hartenberg parameters. The use of an optimal approach makes it possible to define the parameters of the robot and its position and orientation in the environment that satisfy the specified task.>