Static balancing of four-bar compliant mechanisms 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 an approach is useful in the design of quasi-statically balanced fully compliant mechanisms by tuning 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. A full example of the static balancing of two compliant linkages for approximate straight path generation is developed, where actuation energy of the compliant designs is reduced in 66% and 54%, respectively.