Abstract: This paper formulates the planar and spatial versions of an equation that determines one vertex of a triangle in terms of the other two vertices and their interior angles. The fact that a ...

Abstract: Kinematic mappings, which transform the parameters specifying a rigid displacement into a point in a higher dimensional space, have been the focus of recent study for the purpose of classifying ...

Abstract: The dual Euler parameters of a rigid spatial motion are used to define a curve on a dual unit hypersphere. The dual velocity, curvature, and torsion of this curve form a set of instantaneous ...

Abstract: The curvature theory of ruled surfaces has been studied in two different ways. The scalar formulation proceeds by defining a seqeunce of ruled surfaces associated with the trajectory ruled ...

Abstract: This paper examines spherical and 3-spherical rigid motions with instantaneous invariants approaching zero. It is shown that these motions may be identified with planar and spatial motion, ...

Abstract: This paper uses a kinematic mapping of spherical motion to derive an image curve which represents the coupler motion of a doubly folding spherical four bar linkage. The image curve of this ...

Abstract: This paper examines the instantaneous kinematics of motion defined by a parameterized set of 4 × 4 orthogonal matrices, termed hyperspherical motion. The transformation equation defining the ...