A Summary of the Theory and Application of the Conics Method in Robot Kinematics
A summary of the conics method is presented. This method provides a new way to analyze the kinematic geometry of fourth order manipulators. A condition is developed that is sufficient for a fourth order solution to reduce to a quadratic. Applying this condition to a 3R regional manipulator yields seven quadratic robot designs. Several of the derived geometries are sufficiently obscure that their discovery is unlikely without such a systematic approach.
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- Bennett, G.T., “A New Mechanism,” Engineering, 76, 777 (1903).Google Scholar
- Craig, John J., Introduction to Robotics, Addison-Wesley, (1986).Google Scholar
- Graustein, William C., Introduction to Higher Geometry, The MacMillan Company, (1930).Google Scholar
- Korn, G.A. and Korn T.M., Mathematical Handbook for Scientists and Engineers, 2“ Edition, McGraw-Hill, pp. 41–2 (1968).Google Scholar
- Pieper, D.L. and Roth, B., “The Kinematics of Manipulators Under Computer Control,” Proceedings of the 2nd International Congress on the Theory of Machines and Mechanisms, 2, pp. 159–68 (1969).Google Scholar
- Raghavan, M. and Roth, B, B., “Kinematic Analysis of the 6R Manipulator of General Geometry,” 5`h Intl. Symposium on Robotics Research, Tokyo (1989).Google Scholar
- Smith, David R., Design of Solvable 6R Manipulators, Ph.D. Dissertation, Georgia Institute of Technology, 1990.Google Scholar
- Uspensky, J.V., Theory of Equations, McGraw-Hill, (1948).Google Scholar
- Wolfram, S., Mathematica: A System for Doing Mathematics by Computer, Addison Wesley, (1988).Google Scholar