Abstract
In this paper we present a novel dyad dimensional synthesis technique for approximate motion synthesis. The methodology utilizes an analytic representation of the dyad’s constraint manifold that is parameterized by its joint variables. Nonlinear optimization techniques are then employed to minimize the distance from the dyad’s constraint manifold to a finite number of desired locations of the workpiece. The result is an approximate motion dimensional synthesis technique that is applicable to planar dyads. Here, we specifically address planar RR dyads since these are often found in the kinematic structure of industrial robotic systems and mechanisms. These dyads may be combined serially to form a complex open chain or, when connected back to the fixed link, may be joined so as to form a closed chain; e.g. a platform or mechanism. Finally, we present a numerical design case study which demonstrate the utility of the synthesis technique.
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References
Bobrow, J.E., and Park, F.C., (1995), On Computing Exact Gradients for Rigid Body Guidance Using Screw Parameters, Proceedings of the ASME Design Engineering Technical Conferences, vol. 1, pp. 839–844.
Bodduluri, R.M.C., (1990), Design and Planned Movement of Multi-Degree of Freedom Spatial Mechanisms, PhD Dissertation University of California, Irvine.
Bodduluri, R.M.C., and McCarthy, J.M., (1992), Finite Position Synthesis Using the Image Curve of a Spherical Four Bar Motion, ASME Journal of Mechanical Design, vol. 114, pp. 55–60.
Bottema, O., and Roth, B., (1979), Theoretical Kinematics, North-Holland, Amsterdam.
Chirikjian, G.S., (1998), Convolution Metrics for Rigid Body Motion, Proceedings of the ASME Design Engineering Technical Conferences.
Davidon, W., (1959), Variable Metric Method for Minimization, Argonne National Lab., ANL-5990.
Etzel, K.R., and McCarthy, J.M., (1996), A Metric for Spatial Displacements Using Biquaternions on SO(4), Proceedings of the IEEE Robotics and Automation Conferences, vol. 4, pp. 3185–3190.
Fletcher, R., and Powell, M., (1963), A Rapidly-Convergent Method for Minimization, Computer Journal, vol. 6, no. 2.
Ge, Q.J., (1990), The Geometric Representation of Kinematic Constraints in the Clifford Algebra of Projective Space, PhD Dissertation University of California, Irvine.
Gupta, K.C., (1997), Measures of Positional Error for a Rigid Body, ASME Journal of Mechanical Design, vol. 119, pp. 346–348.
Kazerounian, K, and Rastegar, J., (1992), Object Norms: A Class of Coordinate and Metric Independent Norms for Displacements, Proceedings of the ASME Design Engineering Technical Conferences, pp. 271–275.
Larochelle, P., (1994), Design of Cooperating Robots and Spatial Mechanisms, PhD Dissertation University of California, Irvine.
Larochelle, P., (1996), Synthesis of Planar RR Dyads by Constraint Manifold Projection, Proceedings of the ASME Design Engineering Technical Conferences.
Larochelle, P., (1999), On the Geometry of Approximate Bi-Invariant Projective Displacement Metrics, Proceedings of the World Congress on the Theory of Machines and Mechanisms, Oulu, Finland.
Larochelle, P., and McCarthy, J.M., (1995), Planar Motion Synthesis Using an Approximate Bi-Invariant Metric, ASME Journal of Mechanical Design, vol. 117, pp. 646–651.
Larochelle, P., and Tse, D., (1998), A New Method of Task Specification for Spherical Mechanism Design, Proceedings of the ASME Design Engineering Technical Conferences.
Martinez, J.M.R., and Duffy, J., (1995), On the Metrics of Rigid Body Displacements for Infinite and Finite Bodies, ASME Journal of Mechanical Design, vol. 117, pp. 41–47.
McCarthy, J.M., (1990), An Introduction to Theoretical Kinematics, MIT Press.
Park, F.C., (1995), Distance Metrics on the Rigid-Body Motions with Applications to Mechanism Design, ASME Journal of Mechanical Design, vol. 117, no. 1.
Ravani, B., and Roth, B., (1983), Motion Synthesis Using Kinematic Mappings, ASME Journal of Mechanisms, Transmissions, and Automation in Design, vol. 105, pp. 460–467.
Suh, C.H., Radcliffe, C.W., (1978), Kinematics and Mechanism Design, John Wiley and Sons.
Vanderplaats, G., (1984), ADS - A FORTRAN Program for Automated Design Synthesis, Naval Post Graduate School.
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© 2000 Springer Science+Business Media Dordrecht
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Larochelle, P. (2000). Approximate Motion Synthesis Via Parametric Constraint Manifold Fitting. In: Lenarčič, J., Stanišić, M.M. (eds) Advances in Robot Kinematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-4120-8_11
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DOI: https://doi.org/10.1007/978-94-011-4120-8_11
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5803-2
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