Error Analysis for the In-Situ Fabrication of Mechanisms

[+] Author and Article Information
Sanjay Rajagopalan, Mark Cutkosky

Center for Design Research, Stanford University, Palo Alto, CA 94305-2232

J. Mech. Des 125(4), 809-822 (Jan 22, 2004) (14 pages) doi:10.1115/1.1631577 History: Received March 01, 2002; Revised April 01, 2003; Online January 22, 2004
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.


Beaman, J. J., 1997, Solid Freeform Fabrication: A New Direction in Manufacturing—With Research and Applications in Thermal Laser Processing, Kluwer Academic Publishers, Boston.
Chua, C. K., and Fai, L. K., 1997, Rapid Prototyping: Principles and Applications in Manufacturing, Wiley, New York, NY.
Merz, R., Prinz, F. B., Ramaswami, K., Terk, M., and Weiss, L., 1994, “Shape Deposition Manufacturing,” Proceedings of the Solid Freeform Fabrication Symposium, pages 1–8, The University of Texas at Austin, August 8–10.
Bottema, O., and Roth, B., 1979, Theoretical Kinematics, Dover Publications, New York, NY.
Morrison, P., and Morrison, E., 1961, Charles Babbage and His Calculating Engines, Dover Publications, Inc., New York, NY.
Cham, J., Pruitt, B. L., Cutkosky, M. R., Binnard, M., Weiss, L., and Neplotnik, G., 1999, “Layered Manufacturing of Embedded Components: Process Planning Considerations,” Proceedings of the 1999 ASME DETC/DFM Conference, Las Vegas, NV, September 12–15.
Weiss, L. E., Prinz, F. B., Neplotnik, G., Padmanabhan, P., Schultz, L., and Mertz, R., 1996, “Shape Deposition Manufacturing of Wearable Computers,” Proceedings of the Solid Freeform Fabrication Symposium, University of Texas at Austin, August 10–12.
Knappe, L. F., 2000, “Building Around Inserts: Methods for Fabricating Complex Devices in Stereolithography,” Proceedings of the 2000 ASME DETC/DFM Conference, Baltimore, MD, September 10–13.
Mavroidis,  C., DeLaurentis,  K. J., Won,  J., and Alam,  M., 2001, “Fabrication of Non-assembly Mechanisms and Robotic Systems Using Rapid Prototyping,” ASME J. Mech. Des., 123, pp. 516–519, December.
Laliberte, T., Gosselin, C., and Cote, G., 2000, “Rapid Prototyping of Lower-pair, Geared-pair and Cam Mechanisms,” Proceedings of the 2000 ASME Mechanisms and Robotics Conference, Baltimore, MD, September 10–13.
Tuttle,  S. B., 1960, “Error Analysis,” Mach. Des., 32(12).
Knappe,  L. F., 1963, “Technique for Analyzing Mechanism Tolerances,” Mach. Des., 155–157, April 25.
Hartenberg, R. S., and Denavit, J., 1964, Kinematic Synthesis of Linkages, McGraw Hill, New York.
Garrett,  R. E., and Hall,  A. S., 1969, “Effects of Tolerance and Clearance in Linkage Design,” ASME J. Eng. Ind., Series B, 91, pp. 198–202.
Dhande,  S., and Chakraborty,  J., 1973, “Analysis and Synthesis of Mechanical Error in Linkages—A Stochastic Approach,” ASME J. Eng. Ind., Series B, 95, pp. 677–680.
Lakshminarayana, K., and Ramaiyan, G., 1976, “Analysis of the Effects of Errors and Clearances in Mechanisms as a Problem in Statics,” ASME publication 76-DET-67, Proceedings of the ASME DETC, Montreal, Quebec, Canada, September.
Tischler,  C. R., and Samuel,  A. E., 1999, “Prediction of Slop in General Spatial Linkages,” Int. J. Robot. Res., 18(8), 845–858, August.
Denavit,  J., and Hartenberg,  R. S., 1955, “A Kinematic Notation for Lower-pair Mechanisms Based on Matrices,” ASME J. Appl. Mech., pp. 215–221, June.
Fox, R. L., 1971, Optimization Methods for Engineering Design, Addison-Wesley, Mass.
Chakraborty,  J., 1975, “Synthesis of Mechanical Error in Linkages,” Mech. Mach. Theory, 10, pp. 155–165.
Bellman, R., 1957, Dynamic Programming, Princeton University Press, Princeton, NJ.
Fenton,  R. G., Cleghorn,  W. L., and Fu,  J., 1989, “Allocation of Dimensional Tolerances for Multiple Loop Planar Mechanisms,” ASME J. Mech., Transm., Autom. Des., 111, pp. 465–470, December.
Feller, W., 1957, An Introduction to Probability Theory and Its Applications, Vol. 2, Wiley & Sons, New York, NY.
Hayati,  S., and Mirmirani,  M., 1985, “Improving the Absolute Positioning Accuracy of Robot Manipulators,” J. Rob. Syst., 2(4), pp. 397–413.
Suh, C. H., and Radcliffe, C. W., 1978, Kinematics and Mechanism Design, Wiley and Co., New York.
Lin,  P. D., and Chen,  J. F., 1994, “Analysis of Errors in Precision for Closed Loop Mechanisms,” ASME J. Mech. Des., 116, pp. 197–203, March.
Stolfi, J., 1991, Oriented Projective Geometry: A Framework for Geometric Computations, Academic Press, Boston, MA.
Mallik,  A. K., and Dhande,  S. G., 1987, “Analysis and Synthesis of Mechanical Error in Path Generating Linkages Using a Stochastic Approach,” Mech. Mach. Theory, 22(2), pp. 115–123.
Rajagopalan, S., 2000, “Error Analysis and Optimal Pose Selection for the In-situ Fabrication of Mechanisms,” Ph.D. Thesis, Stanford University.
Sommerville, D. M. Y, 1959, Analytical Geometry of Three Dimensions, Cambridge University Press, London.


Grahic Jump Location
Conventional versus in-situ fabrication
Grahic Jump Location
In-situ mechanism prototypes fabricated via Shape Deposition Manufacturing 3: (a) a polymer insect-leg prototype with embedded pneumatic actuator, pressure sensor and leaf-spring joint (b) a hexapedal robot with integrated sensors, actuators and electronics (c) an “inchworm” mechanism, with integrated clutch components, (d) a slider-crank mechanism made from stainless steel. Images courtesy the Stanford Center for Design Research and Rapid Prototyping Laboratories.
Grahic Jump Location
Micromechanisms and devices built using in-situ fabrication techniques. Images courtesy Sandia National Laboratories, SUMMiT(tm) Technologies, www.mems.sandia.gov. Used with permission.
Grahic Jump Location
Comparing conventional and in-situ manufacturing methods—process flow chart. Actions that impart accuracy to the mechanism are specifically identified.
Grahic Jump Location
Modified Denavit-Hartenberg representation for spatial linkages (Lin and Chen, 1994). Note that the specific mechanism shown here is irrelevant—used for illustrative purposes only.
Grahic Jump Location
The effects of link length variation in an assembled 4-bar mechanism
Grahic Jump Location
The effects of joint location variation for an in-situ fabricated 4-bar mechanism
Grahic Jump Location
Frames and notation for the abstract model of in-situ fabrication
Grahic Jump Location
Actual and schematic diagrams of the planar 4-bar crank-rocker mechanism used as an example in this paper. The parameter values are: L1=15 cm,L2=5 cm,L3=25 cm,L4=20 cm,L5=7.5 cm,L6=20 cm (after Mallick and Dhande, 1987). Stochastic simulations on the example are performed with a positional variance σxk2=0.01 cm2. Worst case simulations are performed with a positional variability of 0.3 cm, equivalent to the 3σ stochastic error.
Grahic Jump Location
Multiple positions of the example 4-bar mechanism, corresponding to 30 deg increments of the input angle, θ
Grahic Jump Location
An example build configuration and worst-case variations in joint and coupler point locations
Grahic Jump Location
Worst case coupler-point positional error, plotted on the coupler path
Grahic Jump Location
Total worst-case coupler-point positional errors, plotted against operating angle for four different build configurations, corresponding to different values of the input angle. The error values can be compared with 3σ stochastic errors (see Fig. 17).
Grahic Jump Location
First order estimates of the link-length variance compared to the results of a Monte Carlo simulation
Grahic Jump Location
Pairwise correlation coefficients of the link lengths—first-order results compared to the Monte Carlo simulation
Grahic Jump Location
First order estimates of coupler-point variance for the an in-situ fabricated crank-rocker mechanism (Fig. 9) using conventional stochastic analysis, analysis modified to for in-situ fabrication, and direct Monte Carlo simulation
Grahic Jump Location
Comparison of 3σ stochastic and worst-case (deterministic) error estimates for crank-rocker mechanism
Grahic Jump Location
Convergence rates of Monte Carlo simulations for different operational angles
Grahic Jump Location
Notation for the derivation of modified Denavit-Hartenberg parameters from joint Plücker coordinates.



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