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Research Papers

Kinematic Analysis of a Three-Degree of Freedom Compliant Platform

[+] Author and Article Information
Julio C. Correa

Department of Mechanical Engineering,
Universidad Pontificia Bolivariana,
Medellin 56006, Colombia
e-mail: julio.correa@upb.edu.co

Carl Crane

Department of Mechanical Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: carl.crane@gmail.com

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the Journal of Mechanical Design. Manuscript received May 29, 2012; final manuscript received November 30, 2012; published online April 29, 2013. Assoc. Editor: Craig Lusk.

J. Mech. Des 135(5), 051009 (Apr 29, 2013) (10 pages) Paper No: MD-12-1287; doi: 10.1115/1.4024085 History: Received May 29, 2012; Revised November 30, 2012

This paper addresses the kinematic analysis of a three-degree of freedom (DOF) compliant platform able to move in three dimensional space. The device is formed by the actuators, a central moving platform, and compliant joints. The actuators are three binary links. The moving platform is an equilateral plate. Springs connect the free end of each actuator with each vertex of the central platform. In this way, the motion of the actuators is transmitted to the moving platform. Compliant joints increase the complexity of the motion of the central platform and few studies have been carried out. This paper focuses on the forward and reverse analyses for the platform and the derivation of equations that relate the velocity of the moving platform with the velocity of the actuators.

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Figures

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Fig. 3

Nomenclature for the forward analysis

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Fig. 2

Device in a general position. (a) Top view. (b) Isometric view.

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Fig. 1

Schematic of the device

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Fig. 4

Parameters for the reverse analysis, case 1

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Fig. 5

Location of the local reference systems for the reverse analysis. (a) First rotation. (b) Second rotation.

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Fig. 6

Prescribed vertical component of point P1. (a) Isometric view. (b) Lateral view.

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Fig. 7

Nomenclature for the reverse analysis, case 2. (a) Isometric view. (b) Plane of the forces.

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Fig. 8

Velocity components of the centroid of the moving platform

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