THE INVERSE KINEMATICS OF ROLLING CONTACT OF TIMELIKE CURVES LYING ON TIMELIKE SURFACES
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Date
2019
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Abstract
Rolling contact between two surfaces plays an important role inrobotics and engineering such as spherical robots, single wheel robots, andmulti-Öngered robotic hands to drive a moving surface on a Öxed surface.The rolling contact pairs have one, two, or three degrees of freedom (DOFs)consisting of angular velocity components. Rolling contact motion can bedivided into two categories: spin-rolling motion and pure-rolling motion. Spinrolling motion has three (DOFs), and pure-rolling motion has two (DOFs).Further, it is well known that the contact kinematics can be divided intotwo categories: forward kinematics and inverse kinematics. In this paper, weinvestigate the inverse kinematics of spin-rolling motion without sliding of onetimelike surface on another timelike surface in the direction of timelike unittangent vectors of their timelike tra jectory curves by determining the desiredmotion and the coordinates of the contact point on each surface. We get threenonlinear algebraic equations as inputs by using curvature theory in Lorentziangeometry. These equations can be reduced as a univariate polynomial of degreesix by applying the Darboux frame method. This polynomial enables us toobtain rapid and accurate numerical root approximations and to analyze therolling rate as an output. Moreover, we obtain another outputs: the rollingdirection and the compensatory spin rate.