Static balancing of four-bar linkages with torsion springs by exerting negative stiffness using linear spring at the instant center of rotation

A design approach for the quasi-static balancing of four-bar linkages with torsion springs is proposed. Such approach is useful on the design of statically balanced compliant mechanisms by setting the stiffness of the Pseudo-Rigid-Body-Model. Here the positive stiffness exhibited by torsion springs at the R-joints is compensated by a negative stiffness function. The negative stiffness is created by a non-zero-free-length linear spring connected between the coupler link and the ground, and where both connecting points trace a line directed to the coupler link’s instant center of rotation. An example of the static balancing of the Burmester’s linkage for straight path generation is developed, where actuation energy is reduced in 94% for a range of motion of 80 degrees for the input link.