文档介绍：Available online at hanism
and
Machine Theory
Mechanism and Machine Theory 43 (2008) 201–216
ate/mechmt
A family of spherical parallel manipulators with two legs
Jaime Gallardo a, Ramo´n Rodrı´guez a,*, Martı´n Caudillo a, Jose´ M. Rico b
a Department of Mechanical Engineering, Instituto olo´gico de Celaya, Av. olo´gico y Garcı´a Cubas,
38010 Celaya, Guanajuato, Mexico
b FIMEE, Universidad de Guanajuato, Tampico No. 912, 36730 Salamanca, Guanajuato, Mexico
Received 3 March 2006; received in revised form 6 November 2006; accepted 2 February 2007
Available online 16 April 2007
Abstract
In this work a family of spherical parallel manipulators with a simple architecture is introduced. The primary feature of
this family is to have pact asymmetrical topology consisting of two legs and one spherical joint. This kind of topol-
ogy is in agreement with the parallel manipulator definition of IFToMM – a parallel manipulator ‘‘that controls the
motion of its end effector by means of at least two kinematic chains going from the end effector towards the frame.’’ Ana-
lytical expressions for the forward position, velocity and acceleration of the parallel manipulators have been obtained and
solved for an exemplary manipulator. The forward displacement analysis, free of estrange or undesirable solutions, gives
four possible orientations for the moving platform, which only require less than a second to generate. Afterwards, the
velocity and acceleration analyses are approached by means of the theory of screws. The numerical results from the ana-
lytical expressions are verified paring them to the results from a mechanical system simulation software as if a real
parallel manipulator is being run to collect the position, velocity and acceleration data. Finally, the singularity analysis is
approached in analytic form.
Ó 2007 Elsevier Ltd. All rights reserved.
Keywords: Parallel manipulator; Singularity; Screw theory; Forward kinematics
1. Introduction