[7/7] Duality force/manipulability ellipsoids, robot arm (inverse matrices, dual ellipsoids)

This video concludes the analysis of the force and manipulability ellipsoids (object of videos    • [1/7] manipulability (robotics): jacobian,...   ,    • [5/7] Force ellipsoid, robot arm (1): defi...   , 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 "principal 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 generalization poses a "matrix version" of the basic idea of many mechanisms (lever, gear): multiplying speeds by 7 in a lever divides forces by 7, for example.

The orthogonality of the principal 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.

PLAYLIST:    • Robot arm manipulability/force ellipsoids:...  
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Lectures by Antonio Sala, UPV, Spain
Full collection of videos at: https://personales.upv.es/asala/YT/in...