In other words, planar mechanisms are essentially two dimensional while spatial mechanisms are three dimensional. This tutorial only covers planar mechanisms. 3.2 Kinematics and Dynamics of Mechanisms. Kinematics of mechanisms is concerned with the motion of the parts without considering how the influencing factors (force and mass) affect the. Mechanisms are dealt with in more detail in Chapter 12 Parallel Mechanisms and Robots. 1.2 Position and Orientation Representation Spatial, rigid body kinematics can be viewed as a com-parative study of different ways of representing the pose of a body. Translations and rotations, referred to in com.
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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.