In the present work, a two-link upper limb exoskeleton system is considered with harmonic drive actuators to track a semi-circular and L-shape path. The usage of harmonic drive actuators raises the problem of joint flexibility and produces substantial vibration at the tip of the exoskeleton system. The problem of joint flexibility in the system dynamics is considered using nonlinear spring model. Thereafter, the dynamics for two reduced cases, i.e., linear spring model and the rigid joint model are presented. At the last, transpose Jacobian control strategy is proposed to track the paths with different dynamic models. The controlled joint actuator torques for different cases are found and compared to analyze the system behavior.