With the use of springs, a method to balance the constant forces in arbitrary directions on a planar serial manipulator is developed in this study. Gravity balancing has been discussed a lot in the past. However, manipulators usually bear forces from various directions rather than only a fixed one as gravity. For instance, an industrial manipulator would bear forces from everywhere during the working process. Therefore, a method to balance these forces in arbitrary directions with springs is proposed. Based on the representation of energy, spring energy is the function of springs’ attachment points. Two spring systems with different attachment angles are needed to balance respectively forces in arbitrary directions and gravity. The spring installations of the above systems on 3-DoF manipulators are proposed. Finally, a resistive force-balanced manipulator with/without gravity balance in the grinding process is shown. In sum, this paper for the first time develops the balancing method for forces in arbitrary directions, expanding the spring balance theory to a broader application.
Abstract. This paper proposes a spring efficiency assessment of a statically
spring-balanced planar serial manipulator. The admissible spring configurations for the static balancing of planar serial manipulators without auxiliary links have been determined in the past. Gravity is balanced by the spring configuration systematically; however, the
spring configuration also contains counter-effects between springs.
Conceptually, with fewer counter-effects between springs, there is less
burden on the spring system, which means that the springs are used more
efficiently, and accordingly, the system would be safer, and its service life would be longer. In this study, the spring energy is represented in a
quadratic form. The coefficients in a quadratic form represent the change in elastic energy with the relative position between links, which is named
“elastic pseudo-stiffness”. Compared to the quadratic form of gravity
energy, those elastic pseudo-stiffnesses for static balancing are regarded
as positive contributions of a spring, while those that contain counter-effects are seen as negative ones. Spring efficiency is defined as the ratio of the elastic pseudo-stiffnesses, which has positive contributions for balancing to total elastic pseudo-stiffnesses. To use springs efficiently, the counter-effects, which are functions of spring parameters, need to be decreased, including spring stiffness and the attachment location of springs on links. A method to use spring efficiently by adjusting spring parameters is developed. Furthermore, it is found that, for a spring attached between adjacent links, the spring efficiency is 100 %, and the spring efficiency decreases while the number of joints over which the spring spans increases. In a spring manipulator system, the efficiency is negatively correlated to the payload. As an example, an efficiency assessment on a 3 degrees of freedom (DOF) manipulator is shown at the end.
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