The Monte Carlo method is used to generate the workspaces of manipulators, and the boundary surfaces that separate subspaces having different numbers of configurations (branches); i. e., the singularity surfaces. The method is shown to be simple and readily implementable. It does not use any inverse calculations, and no direct computation of points of singularity is required. The method is naturally suitable for graphical presentation of the geometry of the boundary (singularity) surfaces. The boundary surfaces can be analytically approximated. Limitations on joint motions may be included.
Generation of Manipulator Workspace Boundary Geometry Using the Monte Carlo Method and Interactive Computer Graphics
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Rastegar, J., and Perel, D. (September 1, 1990). "Generation of Manipulator Workspace Boundary Geometry Using the Monte Carlo Method and Interactive Computer Graphics." ASME. J. Mech. Des. September 1990; 112(3): 452–454. https://doi.org/10.1115/1.2912630
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