Kinematic Analysis and Synthesis of Deterministic 3-2-1 Locator Schemes for Machining Fixtures

[+] Author and Article Information
Rodrigo A. Marin, Placid M. Ferreira

Department of Mechanical and Industrial Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801

J. Manuf. Sci. Eng 123(4), 708-719 (Oct 01, 2000) (12 pages) doi:10.1115/1.1381396 History: Received April 01, 2000; Revised October 01, 2000
Copyright © 2001 by ASME
Your Session has timed out. Please sign back in to continue.


Asada,  H., and By,  A. B., 1985, “Kinematic Analysis of Workpart Fixturing for Flexible Assembly with Automatically Reconfigurable Fixtures,” IEEE Journal of Robotics and Automation, RA-1, No. 2, pp. 86–94.
Mani, M., and Wilson, W. R. D., 1988, “Automated Design of Workholding Fixtures Using Kinematic Constraint Synthesis,” Proc. 16th NAMRC of SME, pp. 437–444.
Mani, M., and Wilson, W. R. D., 1988, “Avoiding Interference in 2D Fixture and Grasp Planning,” Proc. ASME Computers in Engineering Conference, pp. 397–402.
Chou,  Y-C., Chandru,  V., and Barash,  M. M., 1989, “A Mathematical Approach to Automatic Configuration of Machining Fixtures: Analysis and Synthesis,” J. Eng. Ind., 111, pp. 299–306.
Bausch, J., and Youcef-Toumi, K., 1990, “Kinematic Methods for Automated Fixture Reconfiguration Planning,” IEEE International Conference on Robotics and Automation, pp. 1396–1401.
DeMeter,  E. C., 1994, “Restraint Analysis of Fixtures Which Rely on Surface Contact,” J. Eng. Ind., 116, pp. 207–215.
Sayeed,  Q. A., and De Meter,  E. C., 1994, “Machining Fixture Design and Analysis Software,” International Journal of Production Research, 32, No. 7, pp. 1655–1674.
De Meter,  E. C., 1993, “Restraint Analysis of Assembly Work Carriers,” Rob. Comput.-Integr. Manufact., 10, pp. 257–265.
De Meter, E. C., 1993, “Selection of Fixture Configuration for the Maximization of Mechanical Leverage,” Manufacturing Science and Engineering, PED-Vol. 64. ASME 1993, pp. 491–506.
Cai,  W., Hu,  S. J., and Yuan,  J. X., 1997, “A Variational Method of Robust Fixture Configuration Design for 3-D Workpieces,” ASME J. Manuf. Sci. Eng., 119, pp. 593–602.
Lee,  K. K., and Cho,  S. H., 1994, “Approaches in Fixture Planning with Friction,” CIRP Ann., 43, No. 1, pp. 331–335.
Lee,  M. R., and Cutkosky,  S. H., 1991, “Fixture Planning with Friction,” Trans. ASME, 113, pp. 320–327.
Goyal,  S., Ruina,  A., and Papadopoulos,  J., 1991, “Planar Sliding with Dry Friction. Part 1. Limit Surface and Moment Function,” Wear, 143, pp. 307–330.
Goyal,  S., Ruina,  A., and Papadopoulos,  J., 1991, “Planar Sliding with Dry Friction. Part 2. Dynamics of Motion,” Wear, 143, pp. 331–352.
Xiuwen,  G., Fuh,  J. Y. H., and Nee,  A. Y. C., 1996, “Modeling of Frictional Elastic Fixture-Workpiece System for Improving Location Accuracy,” IIE Transactions, 28, pp. 821–827.
Rimon,  E., and Burdick,  J. W., 1995, “A Configuration Space Analysis of Bodies in Contact Part I: 1st Order Mobility,” Mechanism and Machine Theory, 30, No. 6, pp. 897–982.
Ohwovoriole,  E. N., 1987, “Kinematics and Friction in Grasping by Robotic Hands,” ASME Journal of Mechanisms, Transmissions and Automation in Design, 109, pp. 398–404.
Ohwovoriole,  M. S., 1981, “An Extension of Screw Theory,” ASME J. Mech. Des., 103, pp. 725–735.
Edelsbrunner, H., 1987, Algorithms in Combinatorial Geometry, Springer-Verlag, Heidelberg.
Hunt, K. H., 1978, Kinematic Geometry of Mechanisms, Clarendon Press, Oxford.
Dobkin, D. P., and Snyder, L., 1979, “On a General Method for Maximizing and Minimizing Among Certain Geometric Problems,” Proceedings 20th IEEE Symposium on the Foundations of Computer Science, pp. 9–17.
Marin, R. A., 2000, The Kinematics of Rigid Body Contact in the Design and Analysis of Machining Fixtures, PhD thesis, University of Illinois at Urbana-Champaign, Department of Mechanical and Industrial Engineering.
Ball, R. S., 1900, A Treatise on the Theory of Screws, Cambridge University Press.
Woo,  L., and Freudentsein,  F., 1970, “Application of Line Geometry to Theoretical Kinematics and the Kinematic Analysis of Mechanical Systems,” J. Mec., 5, pp. 417–460.
Strang, G., 1986, Linear Algebra and its Applications, Harcourt Brace Jovanovich College Publishers, third edition.


Grahic Jump Location
Coordinate system for 3-2-1 locator scheme
Grahic Jump Location
Nondegenerate positioning of w1,w2 and w3 on R1
Grahic Jump Location
Partition induced by a twist on a planar region
Grahic Jump Location
Partition induced by several twists on a planar region
Grahic Jump Location
Coordinate-system-independent condition for w4 and w5
Grahic Jump Location
Partition of boundary and heuristic locator placement in algorithm 3.1. (a) Partition of the boundary of R2. (b) Heuristic location of candidate locator positions.
Grahic Jump Location
Example part with locator faces
Grahic Jump Location
Twist set for example part
Grahic Jump Location
Positioning w4 and w5 on R2
Grahic Jump Location
Final position of locators for example part
Grahic Jump Location
Screw representation of a twist acting on a body B
Grahic Jump Location
Screw representation of a wrench acting on a body B
Grahic Jump Location
(a) Examples of twists that cannot be covered by w4 or w5. (b) Examples of twists that can be covered by w4 or w5.
Grahic Jump Location
Positioning of w1,w2 and w3 on R1



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