Research Papers

Assessing Position Error Due to Clearances and Deformations of Links in Parallel Manipulators

[+] Author and Article Information
Jokin Aginaga

Assistant Professor
Public University of Navarra,
Pamplona, 31006 Spain
e-mail: jokin.aginaga@unavarra.es

Oscar Altuzarra

e-mail: oscar.altuzarra@ehu.es

Erik Macho

Associate Professor
e-mail: erik.macho@ehu.es
University of the Basque Country,
Bilbao, 48013 Spain

Xabier Iriarte

Assistant Professor
Public University of Navarra,
Pamplona, 31006 Spain
e-mail: xabier.iriarte@unavarra.es

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received April 4, 2012; final manuscript received February 4, 2013; published online March 26, 2013. Assoc. Editor: James Schmiedeler.

J. Mech. Des 135(4), 041006 (Mar 26, 2013) (8 pages) Paper No: MD-12-1187; doi: 10.1115/1.4023633 History: Received April 04, 2012; Revised February 04, 2013

Two of the main sources of position error in parallel manipulators are clearances at joints and elastic deformations of the links. The former are usually necessary in order to produce a smooth movement between the pin and the hub of a joint. The latter are unavoidable and they tend to be greater in manipulators designed for pick-and-place tasks due to the need of light links. It can be stated that the end-effector pose error depends on the mechanism configuration, the applied external wrenches, the nature and magnitude of clearances, and the rigidity of the mechanical components. This paper proposes a procedure to calculate position error in parallel manipulators due to both clearances and elastic deformations. Although the procedure is applicable to any planar or spatial parallel manipulator, a planar 5R mechanism is used as an illustrative example in order to make it easier to understand.

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


Merlet, J.-P., 2006, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots,” ASME J. Mech. Des.128(1), pp. 199–205. [CrossRef]
Briot, S., and Bonev, I. A., 2008, “Accuracy Analysis of 3-DOF Planar Parallel Robots,” Mech. Mach. Theory43(4), pp. 445–458. [CrossRef]
Briot, S., and Bonev, I. A., 2010, “Accuracy Analysis of 3T1R Fully Parallel Robots,” Mech. Mach. Theory45, pp. 695–706. [CrossRef]
Altuzarra, O., Pinto, C., Sandru, B., and Hernández, A., 2011, “Optimal Dimensioning for Parallel Manipulators: Workspace, Dexterity, and Energy,” ASME J. Mech. Des., 133 (4), p. 041007. [CrossRef]
Gosselin, C. M., 1990, “Stiffness Mapping for Parallel Manipulators,” IEEE Trans. Robot. Auto., 6(3), pp. 281–290. [CrossRef]
Xu, Q., and Li, Y., 2008, “An Investigation on Mobility and Stiffness of a 3-DOF Translational Parallel Manipulator via Screw Theory,” Robot. CIM Int. Manuf., 24(3), pp. 402–411. [CrossRef]
Ceccarelli, M., and Carbone, G., 2008, “A Stiffness Analysis for CaPaMan (Cassino Parallel Manipulator), Mech. Mach. Theory37(5), pp. 427–439. [CrossRef]
Deblaise, D., Hernot, X., and Maurine, P., 2006, “A Systematic Analytical Method of PKM Stiffness Matrix Calculation,” Proceedings of the IEEE International Conference on Robotics and Automation, 4213–4219, Orlando, FL, May 2006.
Corradini, C., Faroux, J. C., Krut, S., and Company, O., 2003, “Evaluation of a 4-Degree of Freedom Parallel Manipulator Stiffness,” Proceedings of the 11th World Congress in Mechanism and Machine Science, IFTOMM’2003, Tianjin, China, August 2003.
Aginaga, J., Zabalza, I., Altuzarra, O., and Nájera, J., 2012, “Improving Static Stiffness of the 6-RUS Parallel Manipulator Using Inverse Singularities,” Robot. CIM Int. Manuf., 28(4), pp. 458–471. [CrossRef]
Farahanchi, F., and Shaw, S. W., 1994, “Chaotic and Periodic Dynamics of a Slider-Crank Mechanism With Slider Clearance,” J. Sound Vib., 177(3), pp. 307–324. [CrossRef]
Muvengei, O., Kihiu, J., and Ikua, B., 2012, “Numerical Study of Parametric Effects on the Dynamic Response of Planar Multi-Body Systems With Differently Located Frictionless Revolute Clearance Joints,” Mech. Mach. Theory, 53, pp. 30–49. [CrossRef]
Majarena-Bello, A. C., Santolaria-Mazo, J., Samper-Carnicer, D., and Aquilar-Martín, J. J., 2011, “Análisis del Juego, Repetibilidad de Posicionamiento y Precarga de un Mecanismo Paralelo,” Dyna, 86(6), pp. 676–685. [CrossRef]
Bauchau, O. A., and Rodríguez, J., 2002, “Modeling of Joints With Clearance in Flexible Multibody Systems,” Int. J. Solid. Struct., 39(1), pp. 41–63. [CrossRef]
Liu, C.-S., Zhang, K., and Yang, R., 2007, “The FEM Analysis and Approximate Model for Cylindrical Joints With Clearances,” Mech. Mach. Theory, 42 (2), pp. 183–197. [CrossRef]
Tian, Q., Zhang, Y., Chen, L, and Flores, P., 2009, “Dynamics of Spatial Flexible Multibody Systems With Clearance and Lubricated Spherical Joints,” Comput. Struct., 87 (13–14), pp. 913–929. [CrossRef]
Ravn, P., 1998, “A Continuous Analysis Method for Planar Multibody Systems With Joint Clearance,” Multibody System Dynamics, 2, pp. 1–24. [CrossRef]
Flores, P., and Ambrósio, J., 2004, “Revolute Joints With Clearance in Multibody Systems,” Comput. Struct., 82(17–19), pp. 1359–1369. [CrossRef]
Flores, P., Ambrósio, J., Claro, H. C. P., Lankarani, H. M., and Koshy, C. S., 2006, “A Study on Dynamics of Mechanical Systems Including Joints With Clearance and Lubrication,” Mech. Mach. Theory, 41(3), pp. 247–261. [CrossRef]
Flores, P., and Lankarani, H. M., 2012, “Dynamic Response of Multibody Systems With Multiple Clearance Joints,” J. Comput. Nonlinear Dyn., 7(3), p. 031003. [CrossRef]
Khemili, I., and Romdhane, L., 2008, “Dynamic Analysis of a Flexible Slider-Crank Mechanism With Clearance,” Eur. J. Mech. A, 27(5), pp. 882–898. [CrossRef]
Ting, K.-L., Zhu, J., and Watkins, D., 2000, “The Effects of Joint Clearances on Position and Orientation Deviation of Linkages and Manipulators,” Mech. Mach. Theory, 35(3), pp. 391–401. [CrossRef]
Zhu, J., and Ting, K.-L., 2000, “Uncertainty Analysis of Planar and Spatial Robots With Joint Clearances,” Mech. Mach. Theory, 35(9), pp. 1239–1256. [CrossRef]
Jawale, H. P., and Thorat, H. T., 2012, “Investigation of Positional Error in Two Degree of Freedom Mechanism With Joint Clearance,” ASME J. Mech. Robot., 4, p. 011002. [CrossRef]
Venanzi, S., and Parenti-Castelli, V., 2005, “A New Technique for Clearance Influence Analysis in Spatial Mechanisms, ASME J. Mech. Des., 127(3), pp. 446–455. [CrossRef]
Tischer, C. R., and Samuel, A. E., 1999, “Prediction of the Slop in General Spatial Linkages,” Int. J. Robot. Res., 18, pp. 845–858. [CrossRef]
Meng, J., Zhang, D., and Li, Z., 2009, “Accuracy Analysis of Parallel Manipulators With Joint Clearance,” ASME J. Mech. Des., 131(1), p. 011013. [CrossRef]
Innocenti, C., 2002, “Kinematic Clearance Sensitivity Analysis of Spatial Linkages With Revolute Joints,” ASME J. Mech. Des., 124(1), pp. 50–58. [CrossRef]
Lim, S. R., Kang, K., Park, S., Choi, W. C., Song, J.-B., Hong, D., and Shim, J. K., 2002, “Error Analysis of a Parallel Mechanism Considering Link Stiffness and Joint Clearances, KSME Int. J., 16(6), pp. 799–809. [CrossRef]
Tsai, M.-J., and Lai, T.-H., 2008, “Accuracy Analysis of a Multi-Loop Linkage With Joint Clearances,” Mech. Mach. Theory, 43(9), pp. 1141–1157. [CrossRef]
Altuzarra, O., Aginaga, J., Hernández, A., and Zabalza, I., 2011, “Workspace Analysis of Positioning Discontinuities due to Clearances in Parallel Manipulators,” Mech. Mach. Theory, 46(5), pp. 577–592. [CrossRef]
Company, O., Pierrot, F., Krut, S., Baradat, C. and Nabat, V., 2011, “Par2: A Spatial Mechanism for Fast Planar Two-Degree-of-Freedom Pick-and-Place Applications,” Meccanica, 46, pp. 239–248. [CrossRef]


Grahic Jump Location
Fig. 3

Pick-and-place trajectory, velocity, and acceleration for 5R mechanism

Grahic Jump Location
Fig. 2

CAD model of the Par2. Courtesy of Laboratoire d'Informatique, de Robotique et de Microélectronique de Montpellier—University of Montpellier and Foundation Tecnalia.

Grahic Jump Location
Fig. 1

Scheme of the error calculation procedure

Grahic Jump Location
Fig. 4

Pose parameters of a 2 DOF 5R planar parallel manipulator

Grahic Jump Location
Fig. 5

Joint clearances of the 5R planar mechanism

Grahic Jump Location
Fig. 6

Local frames in bars L1 to L4

Grahic Jump Location
Fig. 12

Error due to clearances and elasticity of links with T = 2 s

Grahic Jump Location
Fig. 11

Error due to clearances and elasticity of links with T = 1 s

Grahic Jump Location
Fig. 8

Error due only to clearance

Grahic Jump Location
Fig. 9

Error due only to elasticity

Grahic Jump Location
Fig. 10

Error due to clearances and elasticity of links

Grahic Jump Location
Fig. 7

Nominal and actual trajectories. Errors are amplified by a factor of 50.



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