Higher-Order Path Curvature in Spherical Kinematics

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Abstract
Characteristic numbers are derived which define a spherical curve, within a stretch rotation, to a given order. The loci of all points, which have the same characteristic numbers, under rigid body spherical motion are studied. These results are useful for synthesis and analysis of spherical linkages. The theory is illustrated by numerical examples for the motion of rolling cones and a spherical turning-block linkage.

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