Integrating an exoskeleton as the external apparatus for a brain–machine interface (BMI) has the advantage of providing multiple contact points to determine body segment postures and allowing control to and feedback from each joint. When using macaques as subjects to study the neural control of movement, an upper limb exoskeleton design with unlikely singularity is required to guarantee safe and accurate tracking of joint angles over all possible range of motion (ROM). Additionally, the compactness of the design is of more importance considering macaques have significantly smaller body dimensions than humans. This paper proposes a six degree-of-freedom (DOF) passive upper limb exoskeleton with 4DOFs at the shoulder complex. System kinematic analysis is investigated in terms of its singularity and manipulability. A real-time data acquisition system is set up, and system kinematic calibration is conducted. The effectiveness of the proposed exoskeleton system is finally demonstrated by a pilot animal test in the scenario of a reach and grasp task.