Angular velocity is a vectorial quantity. Angular velocity of a rotating body B in a global frame G is the instantaneous rotation of the body with respect to G about an axis. Using the analytic description of angular velocity, we introduce the velocity and time derivative of homogenous transformation matrices. The transformation matrix GRB is time dependent if a body coordinate frame B rotates continuously with respect to frame G with a common origin. The time dependent rotation matrix will be used to define the angular velocity. To work with angular velocities of relatively moving links, we need to follow the rules of relative derivatives in body and global coordinate frames. Derivative is a frame-dependent operation. Derivative of a vector quantity in the same frame in which the vector is expressed is a simple derivative. Derivative of a vector quantity in another frame other than the frame in which the vector is expressed is a mixed derivative. Considering two frames, we will have two simple and two mix derivatives.


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    Title :

    Angular Velocity


    Contributors:

    Published in:

    Theory of Applied Robotics ; Chapter : 7 ; 361-413


    Publication date :

    2021-12-08


    Size :

    53 pages




    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English





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