This paper studies mappings of spatial kinematics and the geometry for which a spatial displacement is an element. Study’s soma is reviewed and it is shown that Euclidean geometry in three-space with spatial displacements as elements corresponds to elliptic geometry of points in a projective dual three-space. Study’s eight parameters are used to define the mapping of spatial kinematics into points of this projective dual three-space. The basic geometric properties of this dual three-space representation of Study’s soma is developed and it is applied to the study of spatial motions and mechanisms.
Apr 5, 2015 - We present the synthesis of a spherical 4R mechanism for the case of a path. A pure kinematic point of view by minimizing the ACoM. Saha, An optimization technique for the balancing of spatial mechanisms. 1 Physics Intro & Kinematics •Quantities •Units •Vectors •Displacement •Velocity •Acceleration •Kinematics •Graphing Motion in 1-D Some Physics Quantities.