The primary purpose of this study was to design a dynamic system for front chin-ups. Applying the principle of minimum energy expenditure control, this study used this system to simulate the optimal trajectory for angular positions of front chin-ups. Additionally, this study investigated the ways to avoid possible injuries caused by front
chin-ups. The research method of this study involved the following steps: (1) Based on Lagrange-Euler (L-E) equations of motion, this study defined the primary body segments as a dynamic system with 14 degrees of freedom, (2) to achieve the goal of minimum energy control, the Open-loop Linear Quardatic Controller was used. Then under the established boundary conditions, the optimal trajectory for body joints was simulated, (3) the length, mass, center of mass position, and inertia for segments of three subjects were measured, and C++ computer language was used to edit a computer program. The algorithm of the computer program was used to simulate hand suspension motions of three subjects performing front chin-ups. There were two principal findings from the simulation results. First, it was found hat under the established boundary conditions and the control of minimum energy expenditure, the dynamic system can simulate the optimal trajectory for front chin-ups. Second, it was suggested that the three subjects perform a repetition of front chin-up with the time between 1sec and 1.5sec. If the time spent in doing a repetition was longer than
1.5sec, the energy expended would be smaller. However, the time spent in supporting shoulder and elbow joints would become longer, which could easily lead to sore and pain of arm muscles.