Analysis and Passive Control of a Four-Bar Linkage for the Rehabilitation of Upper-Limb Motion

Abstract

In the last two decades robotic rehabilitation research provided significant insight regarding the human-robot interaction, helped understand the process by which the impaired nervous system is retrained to better control movements, and led to the development of a number of mathematical and neurophysiological models that describe both the human motion and the robot control. The human-machine interaction in this research is typically achieved through robotic devices that are based on open kinematic chains. These devices have multiple degrees of freedom (DOF), sophisticated computer control, actuation and sensing. The flexibility of such approach enables the easy implementation of the various models and methods that have to be applied in order to maximize the potential of robotic rehabilitation. On the other hand, mechanisms with fewer DOF’s that are based on closed kinematic chains can generate specific, yet adequate trajectories for the purposes of robotic rehabilitation. An example of such mechanisms is four-bar linkages that have only 1-DOF but yet can generate paths with complex kinematic characteristics. Design and analysis of four-bar linkages is used to achieve a variety of kinematics in terms of trajectory, velocity and acceleration profiles. The simplicity of these mechanisms is appealing and they can be used in rehabilitation due to their ability to replicate the motion of various human joints and limbs. The focus of the current work is to study the use of a four-bar linkage for generating the natural motion of upper-limb reaching tasks with the intention of using this mechanism for rehabilitation. This natural hand motion is described by a straight-line trajectory with a smooth bellshaped velocity profile, which in turn is generated by the well-established Minimum Jerk Model (MJM). The goal is to design passive control elements in a four-bar linkage that generate the required torque for producing the MJM motion. The passive elements are two linear translational springs that act on the driving link of a straight line generating mechanism. A design optimization is used to minimize the difference between the desired and actual input spring torque while remaining within the predefined design space. The final arrangement is simulated in a Multibody Dynamics software that applies feed-forward dynamics to generate the mechanism’s free response to the torque generated by the designed linear springs. The results of this work suggest that systematic design of a four-bar linkage can lead to simple mechanisms that can replicate the natural motion of reaching tasks. Relatively inexpensive linear springs can be employed in the design of passive-active controlled therapeutic mechanisms. Further investigation that combines analysis of both active and passive control/actuation elements must be performed for finalizing the control design. Simulations and analysis that incorporate various impaired hand responses must be also performed in order to finalize the design.