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A Simple Method to Solve the Instantaneous Kinematics of the 5-R$\underbar{P}$UR Parallel Manipulator

Published online by Cambridge University Press:  11 February 2019

Jaime Gallardo-AlvaradoOpen the ORCID record for Jaime Gallardo-Alvarado[Opens in a new window],
Mohammad H. Abedinnasab and
Md. Nazrul Islam
Jaime Gallardo-Alvarado*
Affiliation:
Department of Mechanical Engineering, Instituto Tecnológico de Celaya, TecNM, Celaya 38010, Guanajuato, Mexico
Mohammad H. Abedinnasab
Affiliation:
Department of BiomedicalEngineering, Rowan University, Glassboro, NJ 08028, USA E-mail: abedin@rowan.edu
Md. Nazrul Islam
Affiliation:
College of Computer Sciences and Information Technology, King Faisal University, Al-Hassa 31982, Saudi Arabia E-mail: mnislam@kfu.edu.sa
*
*Corresponding author. E-mail: jaime.gallardo@itcelaya.edu.mx
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Summary

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In this work a simple method to solve the kinematics of the 5-R$\underbar{P}$UR parallel manipulator is introduced. Dealing with the displacement analysis, the kinematic constraint equations required to address the forward–inverse displacement analysis are established according to linear combinations of two vectors attached to the moving platform. Then, besides the solution of the inverse displacement analysis two strategies are proposed in order to solve the forward position analysis. Finally, the input–output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. Numerical examples are provided with the purpose to illustrate the proposed method. Furthermore, the numerical results obtained by means of screw theory are confirmed with the aid of commercially available software.

Keywords

Parallel manipulatorsLimited mobilityKlein formScrew theoryKinematics

Information

Type
Articles
Information
Robotica , Volume 37 , Issue 6 , June 2019, pp. 1143 - 1157
Copyright
© Cambridge University Press 2019 

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