### Unified Dynamics Calculation employing COG Jacobian for Link Mechanisms

Abstract

We show the unified dynamics computation employing Jacobian that relates
the center of gravity (COG Jacobian) to joints of link mechanisms. COG
Jacobian is used for the behavior planning and the control of humanoids.
Also, it usually expresses the relationship between the joints and COG
of a robot's whole body. However, this scheme that is suggested by us calculated
regarding each link and not the robot's whole-body. Moreover, we can obtain
the torques of the active joints in mechanisms by relating COG Jacobian
to the applied forces to COG and by using principle of virtual work. The
COG Jacobian is obtained via the process calculating the accelerations
at COG of links and the equation of motion expressed matrix forms by using
COG Jacobian. Therefore, we can compute the equation of motion of a mechanism
effectively, and the forward dynamics which can be calculated by the obtained
equation. We can calculate the inverse dynamics regardless of open- and
closed-link mechanisms.

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