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.

In the authors' previous paper,10 an input shaping method was presented to reduce motion-induced vibrations effectively for various classes of flexible systems. In this paper, the effectiveness of the shaping method is experimentally demonstrated with a two-link flexible manipulator system

The manipulator for experiments includes two revolute joints and two flexible links, and moves on a vertical plane under gravity. An analytic model is developed considering the flexibility of the system and its joint stiffness in order to derive an appropriate estimation of dynamic modal properties. The input shaping method used in this work utilizes time-varying modal properties obtained from the model instead of the conventional input shaping method which employs time-invariant modal properties. A point-to-point motion is tested in order to show the effectivess of the proposed shaping method in vibration reduction during and after a given motion. The given reference trajectories are shaped to suppress the motion induced vibration. The test results demonstrate that the link vibration can be greatly suppressed during and after a motion, and the residual vibration reduction was observed more than 90% by employing this time-varying impulse shaping technique.

Order-picking, i.e. arranging work-pieces of different types on a pallet, which is nowadays often carried out manually, will in future be more and more automated for economic reasons. The industrial robot in combination with an intelligent gripper, a supporting palletizing and order-picking software and a suitably designed periphery will permit fully automated order-picking. The Fraunhofer-Institute for Manufacturing Engineering and Automation (F.R.G.) has developed such a system which takes advantage of the arrangement of the work-pieces in the compartment stack and simultaneously grips the work-pieces that are then arranged in a pattern on a pallet.

The mass balancing of robotic manipulators has been shown to have favorable effects on their dynamic characteristics. In actual practice, however, since conventional manipulators have flexibility at their joints, the improved dynamic properties obtainable for rigid manipulators may be influenced by those joints flexibilities. This paper investigates the effects of the joints flexibility on the dynamic properties and the controlled performance of a balanced robotic manipulator. The natural frequency distribution and damping characteristics were investigated through frequency response analyses. To evaluate the dynamic performance a series of simulation studies of the open-loop dynamics were made for various trajectories, operating velocities, and joint stiffnesses. These simulations were also carried out for the balanced manipulator with a PD controller situated inside the motor control loop. The results show that, at low speed, the joints flexibility does but little influence the performance of the balanced manipulator, but at high speed it tends to render the balanced manipulator susceptible to vibratory motion and yields large joints deformation errors.

The main objective of this work is to study the performance of a flexible single hub-arm system. The equations of motion are derived using the extended Hamilton principle. The Liapunov functional is used as a condition for the stability analysis. The Liapunov functional is considered as the sum of the internal energy of the flexible beam. The required drive torque was obtained directly through the solution of the inverse dynamic problem. Although the flexible link is nonminimum phase in nature, the use of Liapunov and the PD controller guarantee the causality for the stable case. The effects of tip mass as well as its inertia in the case of stable and asymptotic stable systems were investigated to ensure the validity of this procedure.