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The volume of workspace is a significant kinematic index of parallel manipulator in some applications of engineering. However, the workspace degradation of the manipulator in extreme position is a demanding issue, which results in a fact that such manipulators cannot satisfy the machining requirement of the maximum limit position for the large-scale complex structural components. In this paper, a novel five degrees-of-freedom (DOF) 5PRR+5PUS-PRPU parallel manipulator (PM) is presented. First, the mobility analysis for the proposed manipulator is carried out, and the inverse kinematics as well as the Jacobian matrix is developed. Then, the workspace of the 5PRR+5PUS-PRPU PM and the 5PUS-PRPU PM is analyzed to study the workspace augmentation of the proposed PM. The workspace comparisons of these two PMs prove that the proposed PM not only can realize the large movement of the moving platform along the z-axis, but also possess larger workspace than the 5PUS-PRPU PM when the moving platform has a large movement along the z-axis. Furthermore, the singularity analysis is also conducted to show the singularity-free workspace of the proposed PM. By the introduction of the reconfigurable 5PRR PM, the proposed manipulator effectively augments the reachable workspace of the moving platform along the z-axis and to some extent also solves the issue of workspace degradation of the PM along z-axis.

This paper studies the problem of spatial linkage synthesis for motion generation from the perspective of extracting geometric constraints from a set of specified spatial displacements. In previous work, we have developed a computational geometric framework for integrated type and dimensional synthesis of planar and spherical linkages, the main feature of which is to extract the mechanically realizable geometric constraints from task positions, and thus reduce the motion synthesis problem to that of identifying kinematic dyads and triads associated with the resulting geometric constraints. The proposed approach herein extends this data-driven paradigm to spatial cases, with the focus on acquiring the point-on-a-sphere and point-on-a-plane geometric constraints which are associated with those spatial kinematic chains commonly encountered in spatial mechanism design. Using the theory of kinematic mapping and dual quaternions, we develop a unified version of design equations that represents both types of geometric constraints, and present a simple and efficient algorithm for uncovering them from the given motion.

This paper studies the problem of spherical four-bar motion synthesis from the viewpoint of acquiring circular geometric constraints from a set of prescribed spherical poses. The proposed approach extends our planar four-bar linkage synthesis work to spherical case. Using the image space representation of spherical poses, a quadratic equation with ten linear homogeneous coefficients, which corresponds to a constraint manifold in the image space, can be obtained to represent a spherical RR dyad. Therefore, our approach to synthesizing a spherical four-bar linkage decomposes into two steps. First, find a pencil of general manifolds that best fit the task image points in the least-squares sense, which can be solved using singular value decomposition (SVD), and the singular vectors associated with the smallest singular values are used to form the null-space solution of the pencil of general manifolds; second, additional constraint equations on the resulting solution space are imposed to identify the general manifolds that are qualified to become the constraint manifolds, which can represent the spherical circular constraints and thus their corresponding spherical dyads. After the inverse computation that converts the coefficients of the constraint manifolds to the design parameters of spherical RR dyad, spherical four-bar linkages that best navigate through the set of task poses can be constructed by the obtained dyads. The result is a fast and efficient algorithm that extracts the geometric constraints associated with a spherical motion task, and leads naturally to a unified treatment for both exact and approximate spherical motion synthesis.

In an earlier work, we have combined a curve fitting scheme with a type of shape descriptor, Fourier descriptor (FD), to develop a unified method to the synthesis of planar four-bar linkages for generation of both open and closed paths. In this paper, we aim to extend the approach to the synthesis of planar four-bar linkages for motion generation in an FD-based motion fitting scheme. Using FDs, a given motion is represented by two finite harmonic series, one for translational component of the motion and the other for rotational component. It is shown that there is a simple linear relationship between harmonic content of the rotational component and that of the translational component for a planar four-bar coupler motion. Furthermore, it is shown that the rotational component of the given motion identifies a subset of design parameters of a four-bar linkage including link ratios, while the translational component determines the rest of the design parameters such as locations of the fixed pivots. This leads naturally to a decomposed design space for four-bar mechanism synthesis for approximate motion generation.

This paper deals with the problem of integrated joint type and dimensional synthesis of planar four-bar and six-bar linkages, which could contain both revolute (R) and prismatic (P) joints, for guiding through five specified task positions of the end-effector. In a recent work, we developed a simple algorithm for analyzing a set of given task positions to determine all feasible planar dyads with revolute and/or prismatic joints that can be used to guide through the given positions. This paper extends this algorithm to the integrated joint type and dimensional synthesis of Watt I and II and Stephenson I, II, and III six-bar linkages that contain both R- and P-joints. In the process, we developed a new classification for planar six-bar linkages according to whether the end-effector can be constrained by two dyads (type I), one dyad (type II), or no dyad (type III). In the end, we demonstrate this task-driven synthesis approach with three examples including a novel six-bar linkage for lifting an individual with age disability from seating position to standing position.

This paper presents a single, unified and efficient algorithm for animating the motions of the coupler of all four-bar mechanisms formed with revolute (R) and prismatic (P) joints. This is achieved without having to formulate and solve the loop closure equation associated with each type of four-bar linkages separately. In our previous paper on four-bar linkage synthesis, we map the planar displacements from Cartesian to image space using planar quaternion. Given a set of image points that represent planar displacements, the problem of synthesizing a planar four-bar linkage is reduced to finding a pencil of Generalized- or G-manifolds that best fit the image points in the least squares sense. The three planar dyads associated with Generalized G-manifolds are RR, PR and RP which could construct six types of four-bar mechanisms. In this paper, we show that the same unified formulation for linkage synthesis leads to a unified algorithm for linkage analysis and simulation as well. Both the unified synthesis and analysis algorithms have been implemented on Apple’s iOS platform.Copyright © 2014 by ASME