Post-stroke motor recovery highly relies on voluntarily participating in active rehabilitation as early as possible for promoting the reorganization of the patient's brain. In this paper, a new method is proposed which manipulates cable-based rehabilitation robots to assist multi-joint body motions. This uses an electromyography (EMG) decoder for continuous estimation of voluntary motion intention to establish a cooperative human-machine interface for promoting the participation in rehabilitation exercises. In particular, for multi-joint complex tasks in three-dimensional space, a switching mechanism has been developed which can carve up tasks into separate simple motions. For each simple motion, a linear six-inputs and three-outputs time-invariant model is established respectively. The inputs are the processed muscle activations of six arm muscles, and the outputs are voluntary forces of participants when executing a multi-directional tracking task with visual feedback. The experiments for examining the decoder model and EMG-based controller include model training, testing and controller application phases with seven healthy participants. Experimental results demonstrate that the decoder model with the switching mechanism could effectively recognize arm movement intention and provide appropriate assistance to the participants. This study finds that the switching mechanism can improve both the model estimation accuracy and the completeness for executing complex tasks.