Optimum Design of Serial Robots

An optimum design of an industrial robot can be achieved from different point of views. For example, a robot can be conceived from the standpoint achieving maximum workspace or minimum weight, etc. In this paper, the objective is to arrive at a robot design that will require optimum driving torques/forces at its joints to perform tasks within its workspace. Such a design will automatically save energy. Note that these torques/forces at the joints are highly dependent on the mass and the inertia properties of the robot’s links. Therefore, these quantities were minimized by determining the optimum masses and optimum mass centers and finding out the corresponding inertia properties of the moving links. Such an approach was briefly introduced earlier by the authors with the help of a simple two-link planar arm. In this paper, the concept is generalized and demonstrated with the help of a complex robot, a 6-degrees-of-freedom PUMA robot. To achieve the design for optimum driving torques/forces at the joints, the concept of equimomental system of point masses was introduced, which helped to obtain the optimum locations of the mass centers of each link quite conveniently. However, to compute the driving torques/forces recursively for such equivalent point mass systems, the decoupled natural orthogonal complement matrices for point masses (DeNOC-P) was derived. It has led to a simplified algorithm for obtaining driving torques/forces. The proposed algorithm for optimization is illustrated with the help of a PUMA robot.

Equimomental System and Its Applications

This paper presents a study of an equimomental system and its application. The equimomental system of point-masses for a rigid body moving in plane and space system is studied. Sets of three and seven equimomental point-masses are proposed for a planar and spatial motion, respectively. The set of equimomental point-masses is then applied for the optimization of dynamic performance characteristics of a mechanism, e.g, shaking forces and moments, driving torques, bearing reactions, etc. The Newton-Euler equations of motion of a link undergoing planar motion are formulated systematically in the parameters related to the point-masses, which leads to an optimization scheme for the mass distribution of the links to improve the dynamic performances. The effectiveness of the proposed methodology is shown by applying it to a multiloop mechanism of carpet scrapping machine. A significant improvement in all the dynamic performance characteristics is obtained compared to those of the original mechanism.

Equimomental Tetrads of a Rigid Body

A lamina of mass m can be replaced by an equimomental system of three equal particles m placed at the vertices of a maximum inscribed triangle of a momental ellipse for the centre of mass. Similarly any rigid body can be replaced by an equimomental system of four equal particles (cf. Routh, Elementary Rigid Dynamics, 7th ed. (1905), Art. 44 and Note, p. 423).