This paper proposes a two translational and two rotational (2T2R) four-degrees-of-freedom (DOF) parallel kinematic mechanism (PKM) designed as a knee rehabilitation and diagnosis mechatronics system. First, we establish why rehabilitation devices with 2T2R motion are required, and then, we review previously proposed parallel mechanisms with this type of motion. After that, we develop a novel proposal based on the analysis of each kinematic chain and the Grübler–Kutzbach criterion. Consequently, the proposal consists of a central limb with revolute-prismatic-universal (RPU) joints and three external limbs with universal-prismatic-spherical (UPS) joints. The Screw theory analysis verifies the required mobility of the mechanism. Also, closed-loop equations enable us to put forward the closed-form solution for the inverse-displacement model, and a numerical solution for the forward-displacement model. A comparison of the numerical results from five test trajectories and the solution obtained using a virtual prototype built in msc-adams shows that the kinematic model represents the mechanism's motion. The analysis of the forward-displacement problem highlights the fact that the limbs of the mechanism should be arranged asymmetrically. Moreover, the Screw theory makes it possible to obtain the Jacobian matrix which provides insights into the analysis of the mechanism's workspace. The results show that the proposed PKM can cope with the required diagnosis and rehabilitation task. The results provide the guidelines to build a first prototype of the mechanism which enables us to perform initial tests on the robot.

Although parallel manipulators (PMs) started with the introduction of architectures with 6 Degrees of Freedom (DoF), a vast number of applications require less than 6 DoF. Consequently, scholars have proposed architectures with 3 DoF and 4 DoF, but relatively few 4 DoF PMs have become prototypes, especially of the two rotation (2R) and two translation (2T) motion types. In this paper, we explain the mechatronics design, prototype and control architecture design of a 4 DoF PM with 2R2T motions. We chose to design a 4 DoF manipulator based on the motion needed to complete the tasks of lower limb rehabilitation. To the author's best knowledge, PMs between 3 and 6 DoF for rehabilitation of lower limb have not been proposed to date. The developed architecture enhances the three minimum DoF required by adding a 4 DoF which allows combinations of normal or tangential efforts in the joints, or torque acting on the knee. We put forward the inverse and forward displacement equations, describe the prototype, perform the experimental setup, and develop the hardware and control architecture. The tracking accuracy experiments from the proposed controller show that the manipulator can accomplish the required application.

The need of a device providing two translational (2T) and two rotational (2R) movements led us to the design a 3UPS-1RPU parallel manipulator. The manipulator consisted on a mobile platform connected to a base through four legs. That is, the manipulator layout has one central leg and three external legs at the same radial distance. By studying different locations of the legs anchoring point, we improved the first layout design, yet not the optimal one. On this basis, this paper focus on the optimal dimensional design of the manipulator. To this end, we put forward the kinematics equations of the manipulator in accordance to the anchoring points coordinates. Through a numerical approach, the equations enable to find the manipulator workspace. Also, we find a global manipulability index using a local dexterity measure. The latter index serves as optimal function. The optimization process considers joint constraints. Thus, we built a nonlinear optimization problem solved through sequential quadratic programming algorithms. We start by optimizing only a small set of parameters rather than the entire set, which gives us insights on the initial guess to optimize using the entire set. The optimal design layout varies from the original layout. Findings suggest that a task-oriented reconfiguration strategy can improve manipulator performance.

Nowadays, rehabilitation robots represent a field in which a variety of robotic devices have been proposed. One example of such devices is lower-limb rehabilitation robots. Specifically, the knee joint is one of the joints whose rehabilitation is foreseen as a potential task for a robot device. This paper describes the design of a robot for knee diagnosis and rehabilitation. First, we established the design specification by studying the mobility needed at the robot's end-effector to deal with diagnosis and rehabilitation treatments for knee injuries. The analysis led us to conclude that 4 • of freedom (DoF), two translation (2T) and two rotational (2R), are needed in order to meet the design specifications. After that, we chose a parallel robot with a 3-UPS/RPU architecture from several conceptual designs of 4 DoF (2T2R) parallel robots. For the chosen robot, we developed the inverse kinematic model, and also we established the preliminary dimensions of the robot. Through simulations, we found the workspace of the robot showing that its end-effector is able to follow a prescribed task taken from studying the leg motion. Finally, we built a prototype, which is currently undergoing dynamic modelling, parameter identification and control design stages.

This study proposes a performance index for the dimensional optimization of parallel manipulators with specific tasks. In particular, the index evaluates the dexterity of the mechanism to be designed and compares it with that of the required specific task, e.g., rehabilitation tasks. The proposed index is implemented to design a 3UPS + RPU parallel manipulator for performing physical rehabilitation treatments on lower limbs. First, the condition numbers of both the mechanism and the lower limb are determined. Subsequently, the indexes are compared such that both systems exhibit similar dexterity. As a case study, the approach is implemented in the dimensional synthesis of the 3UPS + RPU parallel manipulator. The optimization approach enables obtaining a dexterity space of the mechanism that best matches that of the lower limb. The results are graphically presented, showing the matching areas of both workspaces, verifying the effectiveness of the proposed index.