Research Papers: Design of Mechanisms and Robotic Systems

Link-Based Performance Optimization of Spatial Mechanisms

[+] Author and Article Information
Yimesker Yihun

Department of Mechanical Engineering,
Idaho State University,
Pocatello, ID
e-mail: yimeyihu@isu.edu

Ken W. Bosworth

Department of Mechanical Engineering,
Idaho State University,
Pocatello, ID
Department of Mathematics,
Idaho State University,
Pocatello, ID
e-mail: boswkenn@isu.edu

Alba Perez-Gracia

Department of Mechanical Engineering,
Idaho State University,
Pocatello, ID
e-mail: perealba@isu.edu

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 24, 2014; final manuscript received July 14, 2014; published online October 20, 2014. Assoc. Editor: Craig Lusk.

J. Mech. Des 136(12), 122303 (Oct 20, 2014) (11 pages) Paper No: MD-14-1190; doi: 10.1115/1.4028304 History: Received March 24, 2014; Revised July 14, 2014

In the design of spatial linkages, the finite-position kinematics is fully specified by the position of the joint axes, i.e., a set of lines in space. However, most of the tasks have additional requirements regarding motion smoothness, obstacle avoidance, force transmission, or physical dimensions, to name a few. Many of these additional performance requirements are fully or partially independent of the kinematic task and can be fulfilled using a link-based optimization after the set of joint axes has been defined. This work presents a methodology to optimize the links of spatial mechanisms that have been synthesized for a kinematic task, so that additional requirements can be satisfied. It is based on considering the links as anchored to sliding points on the set of joint axes, and making the additional requirements a function of the location of the link relative to the two joints that it connects. The optimization of this function is performed using a hybrid algorithm, including a genetic algorithm (GA) and a gradient-based minimization solver. The combination of the kinematic synthesis together with the link optimization developed here allows the designer to interactively monitor, control, and adjust objectives and constraints, to yield practical solutions to realistic spatial mechanism design problems.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Garcia de Jalon, J., and Bayo, E., 1994, Kinematic and Dynamic Simulation of Multibody Systems, Springer-Verlag, Berlin, Germany. [CrossRef]
Minaar, R., Tortorelli, D., and Snyman, J., 2001, “On Nonassembly in the Optimal Dimensional Synthesis of Planar Mechanisms,” Struct. Multidiscip. Optim., 21(5), pp. 345–354. [CrossRef]
Jensen, J., and Hansen, O., 2006, “Dimensional Synthesis of Spatial Mechanisms and the Problem of Non-Assembly,” Multibody Syst. Dyn., 15(2), pp. 107–133. [CrossRef]
Hansen, O., 2002, “Synthesis of Mechanisms Using Time-Varying Dimensions,” Multibody Syst. Dyn., 7(1), pp. 127–144. [CrossRef]
Hobson, M., and Torfason, L., 1975, “Computer Optimization of Polycentric Prosthetic Knee Mechanisms,” Bull. Prosthet. Res., 10, pp. 187–201. [CrossRef]
Jin, D., Zhang, R., Dimo, H., Wang, R., and Zhang, J., 2003, “Kinematic and Dynamic Performance of Prosthetic Knee Joint Using Six-Bar Mechanism,” Rehabil. Res. Dev., 40, pp. 39–48. [CrossRef]
Nokleby, S., and Podhorodeski, R., 1999, “Optimization-Based Synthesis of Grashof Geared Five-Bar Mechanisms,” ASME J. Mech. Des., 123(4), pp. 529–534. [CrossRef]
Kinzel, E., Schmiedeler, J., and Pennock, G., 2006, “Kinematic Synthesis for Finitely Separated Positions Using Geometric Constraint Programming,” Mech. Mach. Theory, 128, pp. 1070–1079.
Cabrera, J., Simon, A., and Prado, M., 2002, “Optimal Synthesis of Mechanisms With Genetic Algorithms,” Mech. Mach. Theory, 37(10), pp. 1165–1175. [CrossRef]
Acharyya, S., and Mandal, M., 2009, “Performance of EAs for Four-Bar Linkage Synthesis,” Mech. Mach. Theory, 44(9), pp. 1784–1794. [CrossRef]
Shieh, W.-B., Tsai, L., and Azarm, S., 1997, “Design and Optimization of a One-Degree-of-Freedom Six-Bar Leg Mechanism for a Walking Machine,” J. Rob. Syst., 14(12), pp. 871–880. [CrossRef]
Yao, J., and Angeles, J., 2000, “Computation of All Optimum Dyads in the Approximate Synthesis of Planar Linkages for Rigid-Body Guidance,” Mech. Mach. Theory, 35(8), pp. 1065–1078. [CrossRef]
Zhou, H., 2009, “Dimensional Synthesis of Adjustable Path Generation Linkages Using the Optimal Slider Adjustment,” Mech. Mach. Theory, 44(10), pp. 1866–1876. [CrossRef]
Shen, Q., Al-Smadi, Y., Martin, P., Russell, K., and Sodhi, R., 2009, “An Extension of Mechanism Design Optimization for Motion Generation,” Mech. Mach. Theory, 44(9), pp. 1759–1767. [CrossRef]
Stock, M., and Miller, K., 2003, “Optimal Kinematic Design of Spatial Parallel Manipulators: Application to Linear Delta Robot,” ASME J. Mech. Des., 125(2), pp. 292–301. [CrossRef]
Arsenault, M., and Boudreau, R., 2004, “The Synthesis of Three-Degree-of-Freedom Planar Parallel Mechanisms With Revolute Joints (3-RRR) for an Optimal Singularity-Free Workspace,” J. Rob. Syst., 21(5), pp. 259–274. [CrossRef]
Altuzarra, O., Hernandez, A., Salgado, O., and Angeles, J., 2009, “Multiobjective Optimum Design of a Symmetric Parallel Schšnflies-Motion Generator,” ASME J. Mech. Des., 131(3), p. 031002. [CrossRef]
Kim, H. S., and Tsai, L.-W., 2003, “Design Optimization of a Cartesian Parallel Manipulator,” ASME J. Mech. Des., 125(1), pp. 43–51. [CrossRef]
Merlet, J., 2006, “Jacobian, Manipulability, Condition Number, and Accuracy of Parallel Robots,” ASME J. Mech. Des., 128(1), pp. 199–206. [CrossRef]
Khan, W., and Angeles, J., 2006, “The Kinetostatic Optimization of Robotic Manipulators: The Inverse and the Direct Problems,” ASME J. Mech. Des., 128(1), pp. 168–178. [CrossRef]
Altuzarra, O., Pinto, C., Sandru, B., and Hernandez, A., 2011, “Optimal Dimensioning for Parallel Manipulators: Workspace, Dexterity, and Energy,” ASME J. Mech. Des., 133(4), p. 041007. [CrossRef]
Chen, C., and Angeles, J., 2006, “Generalized Transmission Index and Transmission Quality for Spatial Linkages,” Mech. Mach. Theory, 42, pp. 1225–1237. [CrossRef]
Wu, C., Liu, X.-J., Wang, L., and Wang, J., 2010, “Optimal Design of Spherical 5R Parallel Manipulators Considering the Motion/Force Transmissibility,” ASME J. Mech. Des., 132(3), p. 031002. [CrossRef]
Ravani, B., and Roth, B., 1983 “Motion Synthesis Using Kinematic Mappings,” ASME J. Mech. Des., 105(3), pp. 460–467.
Hong, B., and Erdman, A., 2005, “A Method for Adjustable Planar and Spherical Four-Bar Linkage Synthesis,” ASME J. Mech. Des., 127(3), pp. 456–463. [CrossRef]
Hayes, M., Luu, T., and Chang, X.-W., 2004, “Kinematic Mapping Application to Approximate Type and Dimension Synthesis of Planar Mechanisms,” Advances in Robot Kinematics, J.Lenarcic and C.Galletti, eds., Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 41–48.
Anoop, M., and Samson, A., 2009, “Optimal Synthesis of Spatial Mechanism Using Genetic Algorithm,” 10th National Conference on Technological Trends (NCTT09), Trivandrum, Kerala, India, Nov. 6–7, pp. 26–32.
Kosinska, A., Galicki, M., and Kedzior, K., 2003, “Design and Optimization of Parameters of Delta-4 Parallel Manipulator for a Given Workspace,” J. Rob. Syst., 20(9), pp. 539–548. [CrossRef]
Lum, M., Rosen, J., Sinanan, M., and Hannaford, B., 2004, “Kinematic Optimization of a Spherical Mechanism for a Minimally Invasive Surgical Robot,” Proceedings of ICRA’04 2004 IEEE International Conference on Robotics and Automation 2004, New Orleans, LA, Apr. 26–May 1, pp. 829–834.
Nielsen, J., and Roth, B., 1998, “Formulation and Solution for the Direct and Inverse Kinematics Problems for Mechanisms and Mechatronics Systems,” Computational Methods in Mechanical Systems, Springer, Berlin, Germany, pp. 33–52.
Niku, S. B., 2001, Introduction to Robotics: Analysis, Systems, Applications, Vol. 7, Prentice Hall, Englewood Cliffs, New Jersey.
Craig, J. J., 1989, Introduction to Robotics, Vol. 7, Addison-Wesley Reading, MA.
Fischer, I., 1998, Dual-Number Methods in Kinematics, Statics and Dynamics, CRC Press, Boca Raton, FL.
Ketchel, J. S., and Larochelle, P. M., 2008, “Self-Collision Detection in Spatial Closed Chains,” ASME J. Mech. Des., 130(9), p. 092305. [CrossRef]
Xiao, J., Xu, J., Shao, Z., Jiang, C., and Pan, L., 2007, “A Genetic Algorithm for Solving Multi-constrained Function Optimization Problems Based on KS Function,” IEEE Congress on Evolutionary Computation2007, CEC 2007, Singapore, Singapore, Sept. 25–28, pp. 4497–4501.
Hayward, V., Choksi, J., Lanvin, G., and Ramstein, C., 1994, “Design and Multi-Objective Optimization of a Linkage for a Haptic Interface,” Advances in Robot Kinematics and Computational Geometry, Springer, Berlin, Germany, pp. 359–368.
Waldron, K. J., and Kinzel, G. L., 2004, Kinematics, Dynamics, and Design of Machinery, 2nd ed., Wiley, New York.
Gfrerrer, A., 2000, “Study’s Kinematic Mapping—A Tool for Motion Design,” Recent Advances in Robot Kinematics, Springer, Dordrecht, The Netherlands, pp. 7–16.
Perez, A., and McCarthy, J. M., 2000, “Dimensional Synthesis of Spatial RR Robots,” Advances in Robot Kinematics, Springer, Dordrecht, The Netherlands, pp. 93–102.
Su, H.-J., Dietmaier, P., and McCarthy, J. M., 2003, “Trajectory Planning for Constrained Parallel Manipulators,” ASME J. Mech. Des., 125(4), pp. 709–716. [CrossRef]
Conn, A., Gould, N., and Toint, Ph. L., 1991, “A Globally Convergent Augmented Lagrangian Algorithm for Optimization With General Constraints and Simple Bounds,” SIAM J. Numer. Anal., 28(2), pp. 545–572. [CrossRef]
Yihun, Y., Miklos, R., Perez-Gracia, A., Reinkensmeyer, D. J., Denney, K., and Wolbrecht, E. T., 2012, “Single Degree-of-Freedom Exoskeleton Mechanism Design for Thumb Rehabilitation,” 2012 Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Zurich, Switzerland, June 29–July 1, pp. 1916–1920.


Grahic Jump Location
Fig. 1

CAD model for manual adjustment and optimization; sliding anchor point from (a) to (b) and from (c) to (d)

Grahic Jump Location
Fig. 2

Overall design strategy. Link-based optimization stages are shown inside the broken lines.

Grahic Jump Location
Fig. 3

Joint axes for two spatial mechanism topologies: (a) a closed linkage, CRR–RRR; (b) a linkage with a tree structure, 3R-(2R,2R)

Grahic Jump Location
Fig. 4

Constraint region represented by a cylindrical surface

Grahic Jump Location
Fig. 5

Constraint region represented by a spherical surface

Grahic Jump Location
Fig. 6

Schematic diagram for the transmission angle

Grahic Jump Location
Fig. 7

Desired trajectory of the CRR–RRR linkage

Grahic Jump Location
Fig. 8

Trajectory for the Bennett linkage

Grahic Jump Location
Fig. 9

Initial CRR-RRR mechanism. Darker lines, corresponding to links, are located at the common normal lines between joints (depicted in a lighter shade).

Grahic Jump Location
Fig. 10

Mechanism obtained after link length constraints used

Grahic Jump Location
Fig. 11

Different configurations of the mechanism obtained after region avoidance constraint is used

Grahic Jump Location
Fig. 12

Mechanism obtained after optimizing region avoidance, overall length and force transmission

Grahic Jump Location
Fig. 13

Motion of the mechanism obtained after optimizing region avoidance, overall length and force transmission. Five positions along the trajectory are reached by the mechanism while avoiding the obstacle (lighter lines corresponding to joint axes, darker lines corresponding to the links, including the end-effector link).

Grahic Jump Location
Fig. 14

The CAD model for the final optimized solution at three different configurations

Grahic Jump Location
Fig. 15

The Bennett linkage used as a hinge and a cabinet door (courtesy of PsiStar Solutions)

Grahic Jump Location
Fig. 16

Initial solution of the Bennett linkage

Grahic Jump Location
Fig. 17

Optimized Bennett linkage with only link length constraints

Grahic Jump Location
Fig. 18

Mechanism with only obstacle avoidance and offset constraint. The blue square corresponds to the cabinet door.

Grahic Jump Location
Fig. 19

Mechanism obtained with link length, offset length, and obstacle avoidance constraints

Grahic Jump Location
Fig. 20

Motion of the final design for the cabinet linkage




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