Lately, there have been numerous applications of computer algebra to special functions used in the various field of science and engineering. In this paper, we consider an efficient algorithm which generates velocity Jacobians for any class of general serial link manipulators in a compact form throughout the effective use of frame transformations. Compared with conventional techniques, a marked improvement of that capability is found in computer algebra applications to one class of a seven-joint manipulator. Together with finding of explicit solutions for joint rates, closed form arm solutions for the desired position of the hand are presented by relating the rotational motion of the elbow to a geometry problem.