Admissible spring configurations for statically balanced planar articulated manipulators have been investigated in previous studies. However, in these spring configurations, springs are only identified by the connection between links. The attachment angles and distance for springs to be properly installed remain unaddressed. In this study, a method to determine attachment angles and distance for springs is developed to ensure all the springs are acting for the benefit of static balancing. Here, the gravitational and elastic potential energies are represented in stiffness matrix form, it is shown that term by term compatibility exists between the first row of gravitational stiffness matrix and the first row of the elastic stiffness matrix. In accordance with these compatibility conditions, the admissible spring attachment angles are found to ensure all the ground-connected springs are acting for the benefit of gravity balancing. And the remained components below the first row of the elastic stiffness matrix are offset by the non-ground-connected springs. In accordance with the compatibility between the remained components and the elastic stiffness matrix of non-ground-connected springs, the spring attachment angles to ensure all the non-ground-connected springs acting for the benefit of elastic balancing are found. The determination of the admissible spring configurations is revisited in addition to the connection between links, and the attachment angles of springs are also specified. The admissible spring configurations of statically balanced planar articulated three- and four-link manipulators are derived. A four-link planar manipulator is used as an example for illustration.
Journal of Mechanisms and Robotics Open Issues