The rehabilitation robot is an application of robotic technology for people with limb disabilities. This paper investigates a new applicable and effective sitting/lying lower limb rehabilitation robot (the LLR-Ro). In order to improve the patient’s training initiative and accelerate the rehabilitation process, a new motion intention acquisition method based on static torque sensors is proposed. This motion intention acquisition method is established through the dynamics modeling of human–machine coordination, which is built on the basis of Lagrangian equations. Combined with the static torque sensors installed on the mechanism leg joint axis, the LLR-Ro can obtain the active force from the patient’s leg. Based on the variation of the patient’s active force and the kinematic functional relationship of the patient’s leg end point, the patient motion intention is obtained and used in the proposed active rehabilitation training method. The simulation experiment demonstrates the correctness of mechanism leg dynamics equations through ADAMS software and MATLAB software. The calibration experiment of the joint torque sensors’ combining limit range filter with an average value filter provides the hardware support for active rehabilitation training. The consecutive variation of the torque sensors from just the mechanism leg weight, as well as both the mechanism leg and the patient leg weights, obtains the feasibility of lower limb motion intention acquisition.