Designing a Translational Parallel Manipulator Based on the 3SS Kinematic Joint

Nowadays, translational parallel manipulators are widely used in industrial applications related to pick and place tasks. In this paper, a new architecture of a translational parallel manipulator without floating prismatic joints and without redundant constraints is presented, which leads to a robust design from the manufacturing and maintenance point of view. The frame configuration has been chosen with the aim of achieving the widest and most regular operational workspace completely free of singularities. Besides, the position equations of the proposed design are obtained in a closed form, as well as the singularity locus. It will be shown that the proposed design owns a very simple kinematics so that the related equations can be efficiently implemented in the control of the robot. In addition, the Jacobian condition number assessment shows that a wide part of the operational workspace is well-conditioned, and also the existence of an isotropic configuration will be proved. Finally, a prototype has been built by following a modular design approach.

Kinematic analysis of the X4 translational–rotational parallel robot

High-speed pick-and-place parallel manipulators have attracted considerable academic and industrial attention because of their numerous commercial applications. The X4 parallel robot was recently presented at Tsinghua University. This robot is a four-degree-of-freedom spatial parallel manipulator that consists of high-speed closed kinematic chains. Each of its limbs comprises an active pendulum and a passive parallelogram, which are connected to the end effector with other revolute joints. Kinematic issues of the X4 parallel robot, such as degree of freedom analysis, inverse kinematics, and singularity locus, are investigated in this study. Recursive matrix relations of kinematics are established, and expressions that determine the position, velocity, and acceleration of each robot element are developed. Finally, kinematic simulations of actuators and passive joints are conducted. The analysis and modeling methods illustrated in this study can be further applied to the kinematics research of other parallel mechanisms.

Kinematic Analysis of a Novel Kinematically Redundant Spherical Parallel Manipulator

This paper introduces a new architecture of spherical parallel robot which significantly extends the workspace when compared to existing architectures. To this end, the singularity locus is studied and the design parameters are chosen so as to confine the singularities to areas already limited by other constraints such as mechanical interferences. First, the architecture of the spherical redundant robot is presented and the Jacobian matrices are derived. Afterwards, the analysis of the singularities is addressed from a geometric point of view, which yields a description of the singularity locus expressed as a function of the architectural parameters. Then, the results are applied to an example set of architectural parameters, which are chosen in order to illustrate the advantages of the redundant architecture over current designs in terms of workspace.

Optimization of the Singularity Locus of a Novel Kinematically Redundant Spherical Parallel Manipulator

This article introduces a new architecture of spherical parallel robot which significantly extends the workspace when compared to existing architectures. To this end, the singularity locus is studied and the design parameters are chosen so as to confine the singularities to areas already limited by other constraints such as mechanical interferences. First, the architecture of the spherical redundant robot is presented and the Jacobian matrices are derived. Afterwards, the analysis of the singularities is addressed from a geometric point of view, which yields a description of the singularity locus expressed as a function of the architectural parameters. Then, the results are applied to an example set of architectural parameters chosen in order to illustrate the advantages of the redundant architecture over current designs in terms of workspace.

Some New Results on the Kinematics of 3R Serial Robots Using Nested Determinants

It has been recently shown that the singularity locus of a 3R robot, and in particular its nodes and cusps, can be algebraically characterized in terms of nested determinants. This neat and structured formulation contrasts with the huge and often meaningless formulas generated using computer algebra systems. In this paper we explore further this kind of formulation. We present two new results which we think are of interest by themselves. First, it is shown how Chrystal’s method, used to obtain the resultant of two quadratic polynomials, can be formulated as nested determinants. Second, it is also shown how the coefficients of the harmonic conic of two given conics, can also be expressed in the same form. These results lead to new formulations for the inverse kinematics of 3R robots, their singularity loci, their nodes, and some of their high-order singularities.

Parallel Robot for Lower Limb Rehabilitation Exercises

The aim of this study is to investigate the capability of a 6-DoF parallel robot to perform various rehabilitation exercises. The foot trajectories of twenty healthy participants have been measured by a Vicon system during the performing of four different exercises. Based on the kinematics and dynamics of a parallel robot, a MATLAB program was developed in order to calculate the length of the actuators, the actuators’ forces, workspace, and singularity locus of the robot during the performing of the exercises. The calculated length of the actuators and the actuators’ forces were used by motion analysis in SolidWorks in order to simulate different foot trajectories by the CAD model of the robot. A physical parallel robot prototype was built in order to simulate and execute the foot trajectories of the participants. Kinect camera was used to track the motion of the leg’s model placed on the robot. The results demonstrate the robot’s capability to perform a full range of various rehabilitation exercises.

A Distance Geometry Approach to the Singularity Analysis of 3R Robots

This paper shows how the computation of the singularity locus of a 3R robot can be reduced to the analysis of the relative position of two coplanar ellipses. Since the relative position of two conics is a projective invariant and the basic projective geometric invariants are determinants, it is not surprising that, using distance geometry, the computation of the singularity locus of a 3R robot can be fully expressed in terms of determinants. Geometric invariants have the benefit of simplifying symbolic manipulations. This paper shows how their use leads to a simpler characterization, compared to previous approaches, of the cusps and nodes in the singularity loci of 3R robots.

Determining the maximal singularity-free circle or sphere of parallel mechanisms using interval analysis

SUMMARYThis paper proposes a systematic algorithm based on the concept of interval analysis to obtain the maximal singularity-free circle or sphere within the workspace of parallel mechanisms. As case studies the 3-RPR planar and 6-UPS parallel mechanisms are considered to illustrate the relevance of the algorithm for 2D and 3D workspaces. To this end, the main algorithm is divided into four sub-algorithms, which eases the understanding of the main approach and leads to a more effective and robust algorithm to solve the problem. The first step is introduced to obtain the constant-orientation workspace and then the singularity locus. The main purpose is to obtain the maximal singularity-free workspace for an initial guess. Eventually, the general maximal singularity-free workspace is obtained. The main contribution of the paper is the proposition of a systematic algorithm to obtain the maximal singularity-free circle/sphere in the workspace of parallel mechanisms. The combination of a maximal singularity-free circle or sphere with the workspace analysis by taking into account the stroke of actuators, as additional constraint to the latter problem, is considered. Moreover, the center point of the circle/sphere is not restrained to a prescribed point.