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TECHNICAL PAPERS

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
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References

Figures

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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.
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The effects of link length variation in an assembled 4-bar mechanism
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The effects of joint location variation for an in-situ fabricated 4-bar mechanism
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Frames and notation for the abstract model of in-situ fabrication
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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.
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Multiple positions of the example 4-bar mechanism, corresponding to 30 deg increments of the input angle, θ
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An example build configuration and worst-case variations in joint and coupler point locations
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Worst case coupler-point positional error, plotted on the coupler path
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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).
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First order estimates of the link-length variance compared to the results of a Monte Carlo simulation
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Pairwise correlation coefficients of the link lengths—first-order results compared to the Monte Carlo simulation
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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
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Comparison of 3σ stochastic and worst-case (deterministic) error estimates for crank-rocker mechanism
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Convergence rates of Monte Carlo simulations for different operational angles
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Notation for the derivation of modified Denavit-Hartenberg parameters from joint Plücker coordinates.
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Comparing conventional and in-situ manufacturing methods—process flow chart. Actions that impart accuracy to the mechanism are specifically identified.
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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.
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Micromechanisms and devices built using in-situ fabrication techniques. Images courtesy Sandia National Laboratories, SUMMiT(tm) Technologies, www.mems.sandia.gov. Used with permission.
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Conventional versus in-situ fabrication

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