A generalized approach for computing the transmission index of parallel mechanisms

Abstract

Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-forprofit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. AbstractThis paper presents a novel approach for computing the transmission index of parallel mechanisms. The approach is based on an extended concept to compute the maximal virtual coefficient, which is an important notion involved in the formulation of dimensionally homogeneous transmission indices for singularity analysis and dimensional optimization of parallel mechanisms. By exploiting the dual property of the virtual coefficient, two characteristic points instead of one as in the current state of the art are defined: one characteristic point is located on the 'floating' axis of the transmission wrench, as in existing approaches, while a second one is located on the floating axis of the output twist of the platform, which is a novel concept. This allows one to define two characteristic lengths, of which the larger is then used for the measure of the "distance" between the transmission wrench screw and the output twist screw. As shown in this paper, this new measure makes it possible to discern more finely the configuration-dependent properties of kinematic performance of parallel mechanisms, thus making it more suitable for dimensional optimization. Confidence in this statement is demonstrated through the comparative study of two in-parallel mechanisms using the new method and previously existing ones.

Review article: Performance measures of parallel kinematics manipulators

“…For example, Yu et al (2008) used a geometric approach to measure the accuracy of 3-DOF planar PKMs. When a manipulator has a complex kinematics, a numerical approach through either the forward or inverse kinematics (Liu and Bonev, 2008) can be used to evaluate the indices. Furthermore, to provide more physical insights, Briot and Bonev (2008) introduced another method to evaluate the indices.…”

Kinematics analysis of a novel over-constrained three degree-of-freedom spatial parallel manipulator

“…If q 1 = q 2 , we can solve for θ and ψ by using Eqs. (24) and (25). The orientation matrix R can be generated, leading to the solution of x, y and z by using Eqs.…”

“…A number of performance indices, such as workspace, dexterity indices, condition number, transmission angle, motion/force transmission indices, et al, have been proposed and applied to the performance evaluation of parallel manipulators [19,[21][22][23][24][25]. As we know, the traditional transmission/pressure angle, which was originally introduced for evaluating the force transmission quality of single-loop linkages, is generally no longer applicable to evaluate the motion/force transmissibility of spatial parallel mechanisms, but for the parallel mechanism proposed in this paper, the two identical RPU limbs are in the same plane and axes of the two revolute joints are parallel to each other, and the axis of revolute joint of the SPR limb is parallel to u axis.…”

Solving the double-banana rigidity problem: a loop-based approach

“…Waldron uses the term "passive degree of freedom" for the same type of motion (Waldron, 1973). However, this term might lead to confusion as in parallel kinematics machines it refers to non-actuated chains (legs) for which the joint variables are dependent functions of actuated ones (Liu et al, 2014). This is also the meaning used in robotics by (Bennett and Hollerbach, 1991) when the joint variables of a virtual contact joint are a function of the actuated robot degrees of freedom.…”