Robot Jacobian

The time acquired of the kinematics equations yields the Jacobian of the robot, which relates the collective ante to the beeline and angular acceleration of the end-effector. The assumption of basic plan shows that the Jacobian aswell provides a accord amid collective torques and the resultant force and torque activated by the end-effector. Atypical configurations of the apprentice are articular by belief its Jacobian.

editVelocity kinematics

The apprentice Jacobian after-effects in a set of beeline equations that chronicle the collective ante to the six-vector formed from the angular and beeline acceleration of the end-effector, accepted as a twist. Specifying the collective ante yields the end-effector aberration directly.

The changed acceleration botheration seeks the collective ante that accommodate a defined end-effector twist. This is apparent by inverting the Jacobian matrix. It can appear that the apprentice is in a agreement area the Jacobian does not accept an inverse. These are termed atypical configurations of the robot.

editStatic force analysis

The assumption of basic plan yields a set of beeline equations that chronicle the resultant force-torque six vector, alleged a wrench, that acts on the end-effector to the collective torques of the robot. If the end-effector bend is known, again a absolute adding yields the collective torques.

The changed statics botheration seeks the end-effector bend associated with a accustomed set of collective torques, and requires the changed of the Jacobian matrix. As in the case of changed acceleration analysis, at atypical configurations this botheration cannot be solved. However, abreast singularities baby actuator torques aftereffect in a ample end-effector wrench. Thus abreast aberancy configurations robots accept ample automated advantage.