On the Computation of the Home Posture of the McGill Schönflies-Motion Generator

The McGill Schönflies-Motion Generator (SMG) is a two-limb parallel robot which is capable of producing three independent translations in the Cartesian space and one rotation about a fixed axis. In this paper, the

home posture

of the McGill SMG, defined as the configuration at which the robot rests, while it is not in operation, is determined. For this matter, the geometry and the velocity analysis of the McGill SMG is recalled from a previous publication. By making intensive use of both linear-algebra identities and results specific to the kinematics of the Schönflies subgroup, the normality conditions associated with the minimization of the condition number of the forward-kinematics Jacobian of the robot are derived in frame-invariant form. This form lends itself to geometric interpretations that would not be possible with lengthy componentwise expressions if commercial algebraic software packages were used.