Research Papers

Synthesis of Spatial Mechanism UR-2SS for Path Generation

[+] Author and Article Information
Wen-Yeuan Chung

Department of Mechanical Engineering,
Chinese Culture University,
Taipei 11114, Taiwan
e-mail: wchung@faculty.pccu.edu.tw

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANISMS AND ROBOTICS. Manuscript received December 3, 2013; final manuscript received December 16, 2014; published online March 23, 2015. Assoc. Editor: Andrew P. Murray.

J. Mechanisms Robotics 7(4), 041009 (Nov 01, 2015) (9 pages) Paper No: JMR-13-1243; doi: 10.1115/1.4029438 History: Received December 03, 2013; Revised December 16, 2014; Online March 23, 2015

This article presents a new spatial mechanism with single degree of freedom (DOF) for three-dimensional path generation. The path can be defined by prescribing at most seven precision points. The moving platform of the mechanism is supported by a U-R (universal-revolute) leg and two S–S (spherical–spherical) legs. The driving unit is the first axis of the universal pair. The U-R leg is synthesized first with the problem of order defects being considered. Precision points then lead to prescribed poses of the moving platform. Two S–S legs are then synthesized to meet these poses. This spatial mechanism with a given input is analogous to a planar kinematic chain so that all possible configurations of the spatial mechanism can be constructed. A strategy consisting of three stages for evaluating branch defects is developed with the aid of the characteristic of double configurations and the technique of coding three constituent four-bar linkages. Two numerical examples are presented to illustrate the design, the evaluation of defects, and the performance of the mechanism.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Suh, C. S., and Radcliffe, C. W., 1978, Kinematics and Mechanisms Design, Wiley, New York.
Russell, K., and Shen, J., 2011, “Planar Four-Bar Motion and Path Generation With Order and Branching Conditions,” J. Adv. Mech. Des., Syst., Manuf., 5(4), pp. 264–273. [CrossRef]
Lin, W. Y., 2010, “A GA-DE Hybrid Evolutionary Algorithm for Path Synthesis of Four-Bar Linkage,” Mech. Mach. Theory, 45(8), pp. 1096–1107. [CrossRef]
Peñuñuri, F., Peón-Escalante, R., Villanueva, C., and Pech-Oy, D., 2011, “Synthesis of Mechanisms for Single and Hybrid Tasks Using Differential Evolution,” Mech. Mach. Theory, 46(10), pp. 1335–1349. [CrossRef]
Matekar, S. B., and Gogate, G. R., 2012, “Optimum Synthesis of Path Generating Four-Bar Mechanisms Using Differential Evolution and a Modified Error Function,” Mech. Mach. Theory, 52, pp. 158–179. [CrossRef]
Cabrera, J. A., Ortiz, A., Nadal, F., and Castillo, J. J., 2011, “An Evolutionary Algorithm for Path Synthesis of Mechanisms,” Mech. Mach. Theory, 46(2), pp. 127–141. [CrossRef]
Zhou, H., and Cheung, H. M., 2002, “Analysis and Optimal Synthesis of Adjustable Linkages for Path Generation,” Mechatronics, 12(7), pp. 949–961. [CrossRef]
Zhou, H., and Ting, K. L., 2002, “Adjustable Slider–Crank Linkages for Multiple Path Generation,” Mech. Mach. Theory, 37(5), pp. 499–509. [CrossRef]
Russell, K., and Sodhi, R. S., 2005, “On the Design of Slider-Crank Mechanisms Part II: Multi-Phase Path and Function Generation,” Mech. Mach. Theory, 40(3), pp. 301–317. [CrossRef]
Peng, C., and Sodhi, R. S., 2010, “Optimal Synthesis of Adjustable Mechanisms Generating Multi-Phase Approximate Paths,” Mech. Mach. Theory, 45(7), pp. 989–996. [CrossRef]
Chiang, C. H., 2000, Kinematics of Spherical Mechanisms, Krieger Publishing Company, Malabar, FL.
Peñuñuri, F., Peón-Escalante, R., Villanueva, C., and Cruz-Villar, C. A., 2012, “Synthesis of Spherical 4R Mechanism for Path Generation Using Differential Evolution,” Mech. Mach. Theory, 57, pp. 62–70. [CrossRef]
Chu, J., and Sun, J., 2010, “Numerical Atlas Method for Path Generation of Spherical Four-Bar Mechanism,” Mech. Mach. Theory, 45(6), pp. 867–879. [CrossRef]
Mullineux, G., 2011, “Atlas of Spherical Four-Bar Mechanisms,” Mech. Mach. Theory, 46(11), pp. 1811–1823. [CrossRef]
Premkumar, P., and Kramer, S., 1990, “Synthesis of Multi-Loop Spatial Mechanisms by Iterative Analysis: The RSSR-SS Path Generator,” ASME J. Mech. Des., 112(1), pp. 69–73. [CrossRef]
Chu, J. K., and Sun, J. W., 2010, “A New Approach to Dimension Synthesis of Spatial Four-Bar Linkage Through Numerical Atlas Method,” ASME J. Mech. Rob., 2(4), p. 041004. [CrossRef]
Marble, S. D., and Pennock, G. R., 2000, “Algebraic-Geometric Properties of the Coupler Curves of the RCCC Spatial Four-Bar Mechanism,” Mech. Mach. Theory, 35(5), pp. 675–693. [CrossRef]
Parikian, T. F., 1997, “Multi-Generation of Coupler Curves of Spatial Linkages,” Mech. Mach. Theory, 32(1), pp. 103–110. [CrossRef]
Huang, C. T., and Lai, C. L., 2012, “Spatial Generalizations of Planar Point-Angle and Path Generation Problems,” ASME J. Mech. Rob., 4(3), p. 031010. [CrossRef]
Krovi, V., Ananthasuresh, G. K., and Kumar, V., 2001, “Kinematic Synthesis of Spatial R-R Dyads for Path Following With Applications to Coupled Serial Chain Mechanisms,” ASME J. Mech. Des., 123(3), pp. 359–366. [CrossRef]
Craig, J. J., 2005, Introduction to Robotics, Prentice Hall, Upper Saddle River, NJ.
Chung, W. Y., 2011, “Hybrid Platform Driven by Low DOF Mechanisms,” 13th World Congress in Mechanism and Machine Science, Guanajuato, Mexico, June 19–23, Paper No. A11_311.
Chiang, C. H., 2000, Kinematics and Design of Planar Mechanisms, Krieger Publishing Company, Malabar, FL.
Chung, W. Y., 2005, “The Position Analysis of Assur Kinematic Chain With Five Links,” Mech. Mach. Theory, 40(9), pp. 1015–1029. [CrossRef]
Ting, K. L., and Dou, X., 1996, “Classification and Branch Identification of Stephenson Six-Bar Chains,” Mech. Mach. Theory, 31(3), pp. 283–295. [CrossRef]
Yan, H. S., and Wu, L. I., 1988, “The Stationary Configurations of Planar Six-Bar Kinematic Chains,” Mech. Mach. Theory, 23(4), pp. 287–293. [CrossRef]


Grahic Jump Location
Fig. 4

Illustration for analogous four-bar linkage

Grahic Jump Location
Fig. 5

Analogous Assur five links

Grahic Jump Location
Fig. 3

Illustration of fixed and moving frames

Grahic Jump Location
Fig. 7

Examples of planar Assur kinematic chain with five links. (a) Configuration 1, (b) configuration 2, and (c) double configurations.

Grahic Jump Location
Fig. 6

Two branches for a planar four-bar linkage

Grahic Jump Location
Fig. 8

Coding of a four-bar linkage at four positions. (a) Code = 1, (b) code = 2, (c) code = 3, and (d) code = 4.

Grahic Jump Location
Fig. 9

Results of example 1. (a) Plot of Δ versus θ1, (b) plot of θ2 versus θ1, and (c) trajectory of point P.

Grahic Jump Location
Fig. 10

Animation picture of the mechanism

Grahic Jump Location
Fig. 13

Results of mechanism BD. (a) Values of criterion, (b) trajectory of point P, and (c) animation picture.

Grahic Jump Location
Fig. 11

Results of mechanism CD. (a) Values of criterion and (b) trajectory of point P.

Grahic Jump Location
Fig. 12

Results of mechanism BC. (a) Values of criterion, (b) trajectory of point P, and (c) animation picture.




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