Mainly drawing on screw theory and linear algebra, this paper presents an approach to determining the bases of three unknown twist and wrench subspaces of lower mobility serial kinematic chains, an essential step for kinematic and dynamic modeling of both serial and parallel manipulators. By taking the reciprocal product of a wrench on a twist as a linear functional, the underlying relationships among their subspaces are reviewed by means of the dual space and dual basis. Given the basis of a twist subspace of permissions, the causes of nonuniqueness in the bases of the other three subspaces are discussed in some depth. Driven by needs from engineering design, criteria, and a procedure are proposed that enable pragmatic, consistent bases of these subspaces to be determined in a meaningful, visualizable, and effective manner. Three typical examples are given to illustrate the entire process. Then, formulas are presented for the bases of the twist/wrench subspaces of a number of commonly used serial kinematic chains, which can readily be employed for the formulation of the generalized Jacobian of a variety of lower mobility parallel manipulators.

(2015) Compliance analysis of a 3-SPR parallel mechanism with consideration of gravity. Mechanism and Machine Theory, 84. Permanent WRAP url:http://wrap.warwick.ac.uk/78035 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.

By drawing on the duality of twist space and wrench space, this paper presents a general and systematic approach for force/motion transmissibility analysis of lower mobility nonredundant and nonoverconstrained parallel manipulators. This leads to the formulation of a complete and justifiable model that enables the force/motion transmissibility analysis to be integrated into a unified framework under the umbrella of a homogenous and decoupled linear transformation that maps the coordinates of the platform wrench/twist in the joint space to its natural coordinates in the operation space. Utilizing the penalty method to avoid the indeterminate form “0/0” when the local maximum of a virtual coefficient approaches zero, a set of dimensionally homogeneous transmission indices is proposed which can be employed for precisely representing the closeness to different types of singularities defined in twist space as well as for dimensional optimization. An example is given to illustrate the effectiveness of this approach.

Drawing mainly on the concepts of dual space and dual basis in linear algebra and on existing screw theory, this paper presents a novel and systematic approach for the force/motion transmissibility analysis of 6DOF parallel mechanisms. By taking the reciprocal product of a wrench on a twist as a linear functional, the property exhibited by the dual basis allows the formulation of the force/motion transmissibility between the joint space and operation space in an accurate and concise manner. The consistency between the force/motion transmissibility and the minimum singular value of the Jacobian for singularity identification is rigorously proved. This leads to the development of a set of homogeneously dimensionless local and global transmission indices for measuring the closeness to singular configurations as well as for kinematic performance evaluation over a given workspace. A Stewart platform is employed an exemplar to illustrate the effectiveness of the approach.

SUMMARY This paper proposes a set of novel indices for evaluating the kinematic performance of a 3-RRS (R and S denote revolute and spherical joint respectively, R denotes active joint.), parallel mechanism whose translational and rotational movements are strongly coupled. First, the indices are formulated using the decoupled overall Jacobian matrix, which is developed using coordinate transformation. Then, the influences of the homogeneous dimensionless parameters on these indices are investigated. In addition, the dimension synthesis of the 3-RRS parallel mechanism is carried out by minimizing the mean value of the kinematic performance indices and their standard deviation. The results demonstrate that the established approach facilitates good global kinematic performance of the parallel mechanism.