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.

Exact Path Synthesis of RCCC Linkages for a Maximum of Nine Prescribed Positions

Abstract

This article addresses the path synthesis of RCCC (revolute-cylindrical-cylindrical-cylindrical) linkages, a problem that has not received due attention in the literature. Compared with planar and spherical four-bar linkages, a RCCC linkage has many more design parameters, which lead to a complex formulation of the path synthesis problem and, consequently, to a quite challenging system of algebraic equations. In this article, the problem is solved with a novel formulation of path synthesis for visiting a number of prescribed positions. This is achieved by means of an alternative coordinate system, which allows point coordinates to be expressed with the aid of two vectors fixed to the same body. By this means, the rotation matrix used to represent the coupler link attitude is obviated. The synthesis equations are then formulated in a simple form. Our formulation confirms that path synthesis admits exact solutions for up to nine prescribed positions, which proves a landmark claim submitted by Burmester. Examples are included to demonstrate the path synthesis procedure with the method thus developed.

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