Kinematic Synthesis of Spherical Four-bar Linkages for Five-Poses Rigid Body Guidance
This paper deals with the kinematic synthesis of spherical four-bar linkages for five-poses rigid body guidance. Particular attention is devoted to the algebraic formulation of the Burmester circlepoint and centerpoint conical surfaces, which are determined for two arbitrary four poses groups among the five assigned poses. The Burmester points are algebraically computed by intersecting each pair of the cubic conical surfaces with the unit sphere in order to synthesize a suitable spherical four-bar linkage. The proposed formulation has been implemented in Matlab and both circlepoint and centerpoint conical surfaces, as well as, the synthesis of a solar tracking spherical four-bar linkage for five-poses rigid body guidance, are presented along with significant results.
KeywordsSpherical Burmester problem spherical four-bar linkages Burmester circle and center -points conical surfaces
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- 2.Burmester L.: Lehrbuch der Kinematik. Arthur Felix Verlag, Leipzig, (1888).Google Scholar
- 5.Suh C.H., Radcliffe C.W.: Kinematics and Mechanisms Design. John Wiley & Sons, New York, (1978).Google Scholar
- 6.Chiang C.H.: Kinematics of Spherical Mechanisms. Cambridge University Press, Cambridge (1988).Google Scholar
- 9.Angeles J., Bai S.: A robust solution of the spherical Burmester problem, ASME IDETC- CIE Conference, Vol. 2: 34th Annual Mechanisms and Robotics Conference, Parts A and B, Montreal, Canada, Paper No. DETC2010-28189, pp. 783-790 (2010).Google Scholar
- 12.Brunnthaler K., Schrëocker H.P., Husty M.: Synthesis of spherical four-bar mechanisms using spherical kinematic mapping. In: J. Lenarcic, B. Roth (eds), Advances in Robot Kinematics, Mechanism and Design, pp. 377–384, Springer, Dordrecht (2006).Google Scholar