Abstract

An analytical formulation for determining the workspace of a point on a body suspended in a Gimbal mechanism is presented. Although the gimbal mechanism comprises three degrees of freedom, the resulting workspace is a region on a spherical surface. The constraint function of the underlying mechanism is studied for singularities using a row-rank deficiency condition of its constraint Jacobian. Singular curves on the resultant spherical surface are determined by a similar analytical criterion imposed on the system’s subjacobian, to compute a set of two joint singularities. These singular curves define regions on the spherical surface that may or may not be accessible. A perturbation technique is then used to identify singular curve segments that are boundary to the workspace region. The methodology is illustrated through a numerical example.

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