The linkage systems have high reliability so that they are preferred as motion-transferring elements for repetitive work.For example, the steering and engine crank systems of an automobile are composed of linkages, exhibiting stable performance.Despite of their usefulness, a fully-automated methodology for designing rigid-body mechanisms is not yet available.Especially, a topology optimization-like unified synthesizing method has not yet been established.The main difficulties are discontinuous Degree-of-freedom (DOF) conditions and nonlinear behavior of linkage systems.Especially, the DOF condition makes problem very difficult to solve.Nevertheless, many approaches have been attempted.Graphical synthesis, analytical method, and numerical optimization were investigated.A method using the spirit of topology optimization has been recently attempted.For instance, a nonlinear finite element method was used to simulate links forming a linkage system1.On the other hand, a spring-connected rigid block approach was proposed to facilitate linkage modeling2.Because aforementioned approaches use gradient-based methods, the expression of DOFs only with continuous design variables is difficult.As a remedy to this problem, a recent study3 suggests two continuous objectivities, which have physical meanings associated with redundancy and deficiency of DOFs, respectively.The one is strain energy for avoiding the DOF deficiency, and the other one, stiffness for preventing DOF redundancy.However, treating these two objectivities with an error value function is still difficult for path generation problems.As a means to overcome the DOF-related problems, an energy transmittance efficiency function is suggested in this study.