Abstract
In this paper, five positions of a planar RPR serial chain are specified and the synthesis equations for two RR constraints are solved to obtain a six-bar linkage. Analysis of the resulting linkage determines if it moves the end-effector smoothly through the five task positions without a branch defect. The design procedure presented randomly selects variations to the positions of the RPR chain in order to obtain new six-bar linkages. This dimensional synthesis algorithm yields a set of six-bar linkages that move the end-effector near the original task positions. This synthesis procedure is applied to the design of a linkage that generates a square pattern. The procedure yielded 122 defect-free linkages for one million iterations.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bagci, C., Burke, D.: Optimum synthesis of coupler curve and uniform rotary motion driven multiloop mechanisms generating complex output motions. J. Mech. Des. 115, 967–977 (1993)
Bawab, S., Kinzel, G.L., Waldron, K.J.: Rectified synthesis of six-bar mechanisms with well-defined transmission angles for four-position motion generation. J. Mech. Des. 118, 377–384 (1996)
Burmester, L.: Lehrbuch der Kinematik. Felix, Leipzig (1886)
Gatti, G., Mundo, D.: Optimal synthesis of six-bar cammed-linkages for exact rigid-body guidance. Mech. Mach. Theory 42, 1069–1081 (2007)
Hartenberg, R.S., Denavit, J.: Kinematic Synthesis of Linkages. McGraw-Hill, New York (1964)
Kinzel, E.C., Schmiedeler, J.P., Pennock, G.R.: Function generation with finitely separated precision points using geometric constraint programming. J. Mech. Des. 129, 1185 (2007)
McCarthy, J.M.: Geometric Design of Linkages. Springer, New York (2000)
Mirth, J.A., Chase, T.R.: Circuit analysis of watt chain six-bar mechanisms. J. Mech. Des. 115, 214–223 (1993)
Plecnik, M.M., McCarthy, J.M.: Five position synthesis of a slider-crank function generator. In: Proceedings of the 2011 International Design Engineering Technical Conferences DETC2011-47581, Washington, DC (2011)
Shiakolas, P.S., Koladiya, D., Kebrle, J.: On the optimum synthesis of six-bar linkages using differential evolution and the geometric centroid of precision positions technique. Mech. Mach. Theory 40, 319–335 (2005)
Soh, G.S., McCarthy, J.M.: The synthesis of six-bar linkages as constrained planar 3R chains. Mech. Mach. Theory 43, 160–170 (2008)
Ting, K., Xue, C., Wang, J., Currie, K.R.: Stretch rotation and complete mobility identification of Watt six-bar chains. Mech. Mach. Theory 44, 1877–1886 (2009)
Watanabe, K., Katoh, H.: Identification of motion domains of planar six-link mechanisms of the Stephenson-type. Mech. Mach. Theory 39, 1081–1099 (2004)
Acknowledgements
The authors acknowledge the support of the National Science Foundation and the assistance of the reviewers. Special thanks to Kevin Hung for executing the design of the screw insertion linkage.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Plecnik, M., McCarthy, J.M. (2013). Dimensional Synthesis of Six-Bar Linkage as a Constrained RPR Chain. In: Viadero, F., Ceccarelli, M. (eds) New Trends in Mechanism and Machine Science. Mechanisms and Machine Science, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4902-3_29
Download citation
DOI: https://doi.org/10.1007/978-94-007-4902-3_29
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4901-6
Online ISBN: 978-94-007-4902-3
eBook Packages: EngineeringEngineering (R0)