This paper presents the constraint dynamic modelling of a six-link elbow-bracing manipulator. This system is kinematically redundant when it is asked to perform spatial trajectory tracking tasks. Hence the extra degrees of freedom (DOFs) can be used to assign additional motion such as constraint forces control without violating end-effect's functions, which can improve the manipulator's performance such as minimizing energy requirements. Since the control of the constraint forces will not affect the end-effect's position, the hybrid force and position control method is proposed. The control scheme consists of two terms: constraint forces control with the incorporation of proportional (p) controller and trajectory tracking control. In addition, the motion equations of motors are incorporated into the constraint dynamics of the system. So that the energy consumption can be calculated by integrating the product of the voltage and current. This study is based on our previous works, which can achieve the control of three constraint forces. Finally, simulation experiments along with comparative studies of previous works such as: with no constraint force and one constraint force are conducted. The results show that the proposed method achieves prior energy-efficient performance and tracking accuracy.