Differential kinematics of serial manipulators using virtual chains

Abstract

This paper presents a new approach to calculate the direct and inverse differential kinematics for serial manipulators. The approach is an extension of the Davies method for open kinematic chains based on a virtual kinematic chain concept introduced in this paper. It is a systematic method that unifies the kinematics of serial manipulators considering the type of kinematics and the coordinate system of the operational space and constitutes an alternative way to solve the differential kinematics for manipulators. The usefulness of the method is illustrated by applying it to an industrial robot

Freedom and Constraint in Coupling Networks

“…Tischler [4] uses the procedure to study special configurations of the RCCC linkage. Campos et al [5] use it in robotics for inverse kinematics and [6] for obstacle detection and avoidance.…”

Virtual kinematic chains to solve the underwater vehicle-manipulator systems redundancy

“…(5) to describe the vehicle's movement, we may choose an open-loop chain with three orthogonal prismatic (P) joints and a spherical (S) one (Fig. 4) in order to represent the movement in a Cartesian reference frame as in (Campos et al, 2005). The first joint of this chain is prismatic and allows the movement between the first link and the base along the X-axis.…”

“…In this paper, we use the virtual kinematic chain concept introduced by Campos (2004), who defines a virtual chain as a kinematic chain composed by links (virtual links) and joints (virtual joints) satisfying the following three properties: a) the virtual chain is open; b) it has joints whose normalized screws are linearly independent; and c) it does not change the mobility of the real kinematic chain.…”

“…In this case the inverse kinematic solution corresponds to the minimization of the vehicle/joint manipulator velocities in a least square sense. This approach is dimensional dependent (Davidson and Hunt, 2004) and the repeatability of the movement in the joints space is not guaranteed (Campos, 2004). Beside this, an approach based on the pseudoinverse (and, consequently, with the same limitations) named Task Priority Redundancy Resolution is widely used in the solution of the inverse kinematics of UVMSs (see Antonelli, 2003, and references therein).…”

Contribución al análisis cinemático y dinámico de manipuladores paralelos

“…Estas velocidades pueden ser de las articulaciones del manipulador o de uno o más eslabones que componen la cadena, y que normalmente corresponden al efector final. La cinemática diferencial también permite el análisis de singularidad, espacio de trabajo e incluso de dexteridad eíndices de desempeño [34] [58] [19].…”