Duality of force/manipulability ellipsoids in a robot (inverse behaviour)

Antonio Sala, UPV

Difficulty: *** ,       Relevance: ,      Duration: 14:43

Summary:

This video concludes the analysis of the force and manipulability ellipsoids (object of videos [elipm1EN], [elipf2EN] and successive ones) of a robot. In this last video, we explore their duality: the main speed and force maneuvers have “inverse” amplitudes: if a maneuver multiplies angular velocity by 7 to obtain end-effector linear velocity, then the same maneuver divides joint torque by 7 to give end-effector force.

For this to be correct, operations must be performed on NON-scaled compatible physical units (m/s, rad/s, N, Nm).

This generalizes to “matrix version” the basic idea of many mechanisms (lever, gear): multiplying speeds by 7 in a lever divides forces by 7, for instance.

The orthogonality of the main SVD maneuvers means that the Jacobian of a robot can be interpreted as an XY table, with two different gear ratios given by the singular values.

*Link to my [ whole collection] of videos in English. Link to larger [ Colección completa] in Spanish.