A unified algorithm to determine the reachable and dexterous workspace of parallel manipulators

This paper presents a novel idea for determining the reachable and dexterous workspace of parallel manipulators. Both the reachable workspace and dexterous workspace are utmost important for optimal design and performance comparison of manipulators, because each configuration or point in this region has specified kinematic dexterity by the designer. We propose a uniform algorithm, called stratified workspace boundary determining algorithm (SWBDA), which considers various physical and contrived constraints. The problems of determining the reachable and dexterous workspace boundaries are defined and the unified method is applied to solve all the problems of this kind. The validity and efficiency of the proposed method are verified with two kinds of representative parallel manipulator, since their relational results were studied in literatures. Finally, the advantages of the proposed method are summarized by comparing with other methods.     

Position,Jacobian and workspace analysis of a 3-PSP spatial parallel manipulator

This paper investigates the problems of kinematics, Jacobian, singularity and workspace analysis of a spatial type of 3-PSP parallel manipulator. First, structure and motion variables of the robot are addressed. Two operational modes, non-pure translational and coupled mixed-type are considered. Two inverse kinematics solutions, an analytical and a numerical, for the two operational modes are presented. The direct kinematics of the robot is also solved utilizing a new geometrical approach. It is shown, unlike most parallel robots, the direct kinematics problem of this robot has a unique solution. Next, analytical expressions for the velocity and acceleration relations are derived in invariant form. Auxiliary vectors are introduced to eliminate passive velocity and acceleration vectors. The three types of conventional singularities are analyzed. The notion of non-pure rotational and non-pure translational Jacobian matrices is introduced. The non-pure rotational and non-pure translational Jacobian matrices are combined to form the Jacobian of constraint matrix which is then used to obtain the constraint singularity. Finally, two methods, a discretization method and one based on direct kinematics are presented and robot non-pure translation and coupled mixed-type reachable workspaces are obtained. The influence of tool length on workspace is also studied.     

Mobility properties of a Schoenflies-type parallel manipulator

This paper addresses the mobility properties of a novel Schoenflies-type parallel manipulator. By analyzing the degree of freedom (DoF) of the manipulator, we select a set of independent variables to describe the pose relationship of the manipulator and the fixed base, which is the least in number compared with others. Through coordinate transformation, we can obtain the geometric relationship in the absolute coordinate system via a set of parametric equations. As a result, the least order's Jacobian matrix will be gained and the singularity of the manipulator can be expressed as the determinate of the Jacobian matrix is zero. The distinctive merit of this methodology is that the order of Jacobian matrix is the least compared with others.     

Design of cable-driven parallel manipulators for a specific workspace using interval analysis

In this paper, we present a method, based on interval analysis, to solve the problem of designing cable-driven parallel manipulators (CDPMs) for a desired workspace. The constraint of having positive cable tensions ensuring the equilibrium of the platform has to be satisfied within the given workspace. The proposed algorithm is based on interval analysis, which covers the entire workspace and hence guarantees a singularity-free workspace. Furthermore, the algorithm is capable of finding all possible solutions for this problem and an optimal one is selected according to the user-defined criterion. Two examples are selected to show the efficiency of the developed algorithm in solving this complex problem. The first one deals with the design of a planar CDPM and the second one considers a spatial CDPM. In both cases, the algorithm succeeded to find all possible designs from which the designer can select a solution that fits best his application.     

Dynamics analysis for a novel 6-DoF parallel manipulator I with three planar limbs

A novel 6-DoF parallel manipulator I with three planar limbs is proposed and its dynamics is analyzed systematically. First, its characteristics and DoF are analyzed and calculated. Second, the formulae for solving kinematics of the moving platform and the planar limbs are derived. Third, the formulae for solving the inertial wrench applied on the planar limbs and the moving platform are derived, and dynamics formula is derived for solving dynamic active forces applied onto the planar limbs. Fourth, a singularity of the proposed parallel manipulator is determined and analyzed. Fifth, an analytic example is given for solving the kinetostatics and dynamics of the proposed parallel manipulator, and the solved results are analyzed and verified by the simulation mechanism. Finally, a workspace is constructed and analyzed by comparing with an existing 6-DoF parallel manipulator.