The exoskeleton of the upper limb is an external parallel kinematic chain to the human arm. The device is designed to apply a specific torque of interaction to the human body resulting from bilateral teleoperation or rehabilitation. Its task is to work comfortably with the human arm. This paper presents the structure of the developed device and the control system of its joints. The construction of the joints’ drive system was performed based on the Bowden cable transmission. Based on the Bowden cable flexibility, it is possible to control the generated drive torque following the serial elastic actuator concept. The article presents joint control methods minimizing the influence of friction in the closed-loop Bowden cable conduit system. We also present the methods of estimating the torque of interaction with the operator based on the ExoArm 7-DOF exoskeleton dynamics model.