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and
Machine Theory
Mechanism and Machine Theory 43 (2008) 918–927
ate/mechmt
Inverse dynamics of a ary gear train for robotics
Stefan Staicu *
Department of Mechanics, University ‘‘Politehnica’’ of Bucharest, 313 Splaiul Independentei, Bucharest, Romania
Received 24 February 2007; received in revised form 31 May 2007; accepted 12 June 2007
Available online 3 August 2007
Abstract
Recursive matrix relations concerning the geometric analysis, kinematics and dynamics of a Bendix wrist ary
bevel-gear train for robotics are established in the paper. The prototype of this mechanism is a 3-DOF system with seven
links and four bevel gear pairs controlled by electric motors. Supposing that the rotational motion of the platform is
known, an inverse dynamic problem is developed using the principle of virtual powers. Some relations and graphs for tor-
ques and powers of three actuators are determined.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Dynamics; ary gear train; Virtual powers
1. Introduction
A robot manipulator needs at least six degrees of freedom to manipulate an object freely in space. The first
three moving links are used primarily for manipulating the position, while the second mechanism is used for
controlling the orientation of the end-effectors. The subassembly associated with the last moving links is called