文档介绍：Available online at hanism
and
Machine Theory
Mechanism and Machine Theory 43 (2008) 1268–1280
ate/mechmt
The algebraic synthesis of a spatial TS chain
for a prescribed acceleration task
Nina Patarinsky Robson a,*, J. Michael McCarthy a, Irem Y. Tumer b
a Robotics and Automation Laboratory, University of California, Irvine, CA 92697, United States
plex System Design Laboratory, Oregon State University, Corvallis, OR 97331, United States
Received 5 October 2006; received in revised form 4 October 2007; accepted 25 October 2007
Available online 20 February 2008
Abstract
In this paper, we formulate and solve the algebraic synthesis equations for a TS serial chain, which is a 5R chain formed
so that the first two joint axes intersect at right angles, the T joint, and the last three joints have axes that intersect in a
point, forming the S joint. The task for this chain is to have a prescribed acceleration for the end-effector movement.
In this case, we show that there are two basic cases for the synthesis problem: (i) tasks in which one acceleration is specified;
and (ii) tasks that have two specified accelerations. The polynomial systems for these two cases are shown to have 30 and
38 roots, and we present a polynomial elimination procedure that yields in 30 and 44 roots, respectively. An example is
presented that positions a robot arm, in which the elbow joint has failed, in order to plish a given task.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Robot kinematics; TS chain synthesis; Spatial linkage synthesis; Robot path planning
1. Introduction
This paper considers the synthesis of a spatial TS serial chain such that it guides a floating link through a set
of positions with specified accelerations. We find that the acceleration constraint equations increase -
plexity of the algebraic elimination process.
The TS chain has seven design parameters, the coordinates of the center of the intersection of the perpen-
dicular revolute