A Darboux-Frame-Based Formulation of Spin-Rolling Motion of Rigid Objects with Point Contact
MetadataShow full item record
This paper investigates the kinematics of spin-rolling motion of rigid objects. This paper does not consider slipping but applies a Darboux frame to develop kinematics of spin-rolling motion, which occurs in a nonholonomic system. A new formulation of spin-rolling motion of the moving object is derived in terms of contravariant vectors, rolling velocity, and geometric invariants, including normal curvature, geodesic curvature, and geodesic torsion of the respective contact curve. The equation is represented with geometric invariants. It can be readily generalized to suit both arbitrary parametric surface and contact trajectory and can be differentiated to any order. Effect of the relative curvatures and torsion on spin-rolling kinematics is explicitly presented. The translation velocity of an arbitrary point on the moving object is also derived based on the Darboux frame.
©2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Showing items related by title, author, creator and subject.
Cui, Lei; Dai, J. S. (2010)This paper applies Darboux frame method to developing geometric kinematics of sliding-spin-rolling motion of rigid objects with point contact. For the first time, the geodesic curvatures, normal curvatures and geodesic ...
Cui, Lei; Dai, J. (2015)Rolling contact has been used by robotic devices to drive between configurations. The degrees of freedom (DOFs) of rolling contact pairs can be one, two, or three, depending on the geometry of the objects. This paper aimed ...
Cui, Lei; Dai, J. (2015)The adjoint approach has proven effective in studying the properties and distribution of coupler curves of crank-rocker linkages and the geometry of a rigid object in spatial motion. This paper extends the adjoint approach ...