Gravity compensation of parallel kinematics mechanism using torsional springs based on potential energy optimization

Passive gravity compensation for a mechanism is usually preferred to the active one for some reasons including cost consideration. Many technologies based on counterweight and linear springs have been widely developed, whereas the use of torsional springs is rarely discussed due to unavailability of exact mathematical manipulation to determine the required spring constants to achieve the static balance. This paper proposes the use of torsional springs for passive gravity compensation applied to a parallel kinematics mechanism. The spring constants are determined by constrained optimization approach aiming at minimizing the total potential energy of the mechanism along a prescribed trajectory within the range of motion. It is shown that the solution provides almost-statically-balanced state of the mechanism within its range of motion. This accordingly reduces the required actuation forces/torques and hence the power consumption.