... ′ R , H R , and R R mechanisms. 20 10 2007 03 08 2009 04 08 2009 16 09 2009 Gaussian distribution robot kinematics circular surface lines of curvature Euclidean invariants mechanisms kinematics differential geometry robotics workspace While mechanisms...

...Yi-Pei Shih; Zhang-Hua Fong; Grandle C. Y. Lin Based on the theory of gearing and differential geometry, a universal hypoid generator mathematical model for face hobbing spiral bevel and hypoid gears has been developed. This model can be used to simulate existing face hobbing processes...

...Yi Zhang; Kwun-Lon Ting This paper presents a study on the higher-order motion of point-lines embedded on rigid bodies. The mathematic treatment of the paper is based on dual quaternion algebra and differential geometry of line trajectories, which facilitate a concise and unified description...

... of a parametric surface used in this formulation, is determined from the first and second fundamental forms adapted from differential geometry. Definiteness properties of a quadratic form developed from the acceleration analysis determine admissible normal movements. For singular surfaces resulting from active...

... using methods of differential geometry. The components of the tensor with respect to a basis of twists are given by evaluating the tensor on a pair of basis twists. We show that this tensor depends on the choice of an affine connection on the Lie group, SE 3 . In addition, we show that the definition...

.... That is, when one surface is given, a couple of principal curvatures 1 / ρ i ′ , 1 / ρ i ″ and angle δ i which indicate the principal direction of the surface at the mean point will be determined by differential geometry. Therefore, if one side of the two...

.... 01 July 1998 manipulator kinematics differential geometry robot kinematics Evaluation of singularities plays an important role in several aspects of robotics including design, trajectory planning, and control. Much of the past research in the area of singularities of manipulators...

...Ningxin Chen, Manager of Research, Ph.D. The presented paper utilizes the basic theory of the envelope surface in differential geometry to investigate the undercutting line, the contact boundary line and the limit normal point of conjugate surfaces in gearing. It is proved that (1) the edges...