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.

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Fuller, R., 1975, Synergetics, Explorations in the Geometry of Thinking, Collier Macmillan, London.
Kenner, H., 1976, Geodesic Math and How to Use It, University of California Press, Berkeley, CA.
Calladine, C., 1978, “Buckminster Fuller's Tensegrity Structures and Clerk Maxwell's Rules for the Construction of Stiff Frames,” Int. J. Solids Struct., 14, pp. 161–172. [CrossRef]
Murakami, H., 2001, “Static and Dynamic Analyses of Tensegrity Structures. Part 1. Nonlinear Equations of Motion,” Int. J. Solids Struct., 38, pp. 3599–3613. [CrossRef]
Crane, C., Duffy, J., and Correa, J., 2005, “Static Analysis of Tensegrity Structures,” ASME J. Mech. Des., 127(2), pp. 257–268. [CrossRef]
Knight, B. F., 2000, “Deployable Antenna Kinematics Using Tensegrity Structure Design,” Ph.D. thesis, University of Florida, Gainesville, FL.
Sultan, C., and Corless, M., 2000, “Tensegrity Flight Simulator,” J. Guid. Control Dyn., 23(6), pp. 1055–1064. [CrossRef]
Tibert, A., and Pellegrino, S., 2002, “Deployable Tensegrity Reflectors for Small Satellites,” J. Spacecr. Rockets, 39(5), pp. 701–709. [CrossRef]
Sultan, C., and Skelton, R., 2004, “A Force and Torque Tensegrity Sensor,” Sens. Actuators A, 112(2–3), pp. 220–231. [CrossRef]
Ingber, D., 2003, “Tensegrity I. Cell Structure and Hierarchical Systems Biology,” J. Cell. Sci., 116, pp. 1157–1173. [CrossRef] [PubMed]
Fest, E., Shea, K., Domer, B., and Smith, F. C., 2003, “Adjustable Tensegrity Structures,” J. Struct. Eng., 129(4), pp. 515–526. [CrossRef]
Sultan, C., and Skelton, R., 2003, “Deployment of Tensegrity Structures,” Int. J. Solids Struct., 40, pp. 4637–4657. [CrossRef]
Arsenault, M., and Gosselin, C. M., 2006, “Kinematic, Static and Dynamic Analysis of a Planar 2-DOF Tensegrity Mechanism,” Mech. Mach. Theory, 41, pp. 1072–1089. [CrossRef]
Arsenault, M., 2011, “Stiffness Analysis of a 2DOF Planar Tensegrity Mechanism,” J. Mech. Rob., 3(2), p. 021011. [CrossRef]
Hernandez, S., and Mirats, J., 2008, “Tensegrity Frameworks: Static Analysis Review,” Mech. Mach. Theory, 43, pp. 859–881. [CrossRef]
McCarthy, J. M., 2011, “21st Century Kinematics: Synthesis, Compliance, and Tensegrity,” J. Mech. Rob., 3(2), p. 020201. [CrossRef]
Pelesko, J., and Bernstein, D., 2002, Modeling MEMS and NEMS, CRC Press, Boca Raton, FL.
Ebefors, T., Mattsson, J., Kalvesten, E., and Stemme, G., 1999, “A Robust Micro Conveyer Realized by Arrayed Polymide Joint Actuators,” Proceedings of the 12th IEEE Conference on Micro Electro Mechanical Systems, Orlando, FL, pp. 576–581.
Suh, J., Darling, R., Bohringer, K., Donald, B., Baltes, H., and Kovacs, G., 1999, “CMOS Integrated Ciliary Actuator Array as a General-Purpose Micromanipulation Tool for Small Objects,” J. Microelectromech. Syst., 8(4), pp. 483–496. [CrossRef]
Chen, S., and Culpepper, M. L., 2006, “Design of a Six-Axis Micro-Scale Nanopositioner-uHexFlex,” Precis. Eng., 30, pp. 314–324. [CrossRef]
Brower, D. M., De Jong, B. R., and Soemers, H. M. J. R., 2010, “Design and Modeling of a Six DOFs MEMS-Based Precision Manipulator,” Precis. Eng., 34, pp. 307–319. [CrossRef]
Bamberger, H., and Shoham, M., 2007, “A Novel Six Degrees-of-Freedom Parallel Robot for MEMS Fabrication,” IEEE Trans. Rob., 23(2), pp. 189–195. [CrossRef]
Liang, Q., and Zhang, D., 2010, “Micromanipulator With Integrated Force Sensor Based on Compliant Parallel Mechanism,” Proceedings of the 2010 IEEE International Conference on Robotics and Biomimetics, Tianjin, China, pp. 709–714.
Brand, L., 1947, Vector and Tensor Analysis, Wiley, New York.
Duffy, J., 1996, Statics and Kinematics With Applications to Robotics, Cambridge University, New York.
Crane, C., and Duffy, J., 1998, Kinematic Analysis of Robot Manipulators, Cambridge University, New York.
Crane, C., Rico, J., and Duffy, J., 2007, Screw Theory and its Application to Spatial Robot Manipulators, University of Florida, Gainesville, FL.
Tsai, L., 1999, Robot Analysis, Wiley, New York.


Grahic Jump Location
Fig. 3

Nomenclature for the forward analysis

Grahic Jump Location
Fig. 2

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

Grahic Jump Location
Fig. 1

Schematic of the device

Grahic Jump Location
Fig. 4

Parameters for the reverse analysis, case 1

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
Fig. 6

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

Grahic Jump Location
Fig. 7

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

Grahic Jump Location
Fig. 8

Velocity components of the centroid of the moving platform



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In