Latest Papers

ASME Journal of Mechanisms and Robotics

  • Dynamics of Mobile Manipulators Using Dual Quaternion Algebra
    on September 14, 2022 at 12:00 am

    AbstractThis article presents two approaches to obtain the dynamical equations of mobile manipulators using dual quaternion algebra. The first one is based on a general recursive Newton–Euler formulation and uses twists and wrenches, which are propagated through high-level algebraic operations and works for any type of joints and arbitrary parameterizations. The second approach is based on Gauss’s Principle of Least Constraint (GPLC) and includes arbitrary equality constraints. In addition to showing the connections of GPLC with Gibbs–Appell and Kane’s equations, we use it to model a nonholonomic mobile manipulator. Our current formulations are more general than their counterparts in the state of the art, although GPLC is more computationally expensive, and simulation results show that they are as accurate as the classic recursive Newton–Euler algorithm.

A Mobility Determination Method for Parallel Platforms Based on the Lie Algebra of SE (3) and Its Subspaces


This contribution presents a screw theory-based method for determining the mobility of fully parallel platforms. The method is based on the application of three stages. The first stage involves the application of the intersection of subalgebras of Lie algebra, se(3), of the special Euclidean group, SE(3), associated with the legs of the platform. The second stage analyzes the possibility of the legs of the platform generating a sum or direct sum of two subalgebras of the Lie algebra, se(3). The last stage, if necessary, considers the possibility of the kinematic pairs of the legs satisfying certain velocity conditions; these conditions reduce the platform’s mobility analysis to one that can be solved using one of the two previous stages. Several examples are illustrated.
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