Dynamic Performance Analysis of Minimally Actuated 4-Bar Linkages for Upper Limb Rehabilitation

Abstract

In the last two decades robotic rehabilitation research provided insight regarding the human-robot interaction, helped understand the process by which the impaired nervous system is retrained to better control the hand motion, and led to the development of a number of mathematical and neurophysiological models that describe both the hand motion and the robot control. Now that this pool of knowledge is available, the respective models can be applied in a number of ways outside the robot domain, in which, machines are based on open kinematic chains with n-degrees of freedom (DOF’s) and sophisticated computer control, actuation and sensing. One such example is the use of mechanisms, closed kinematic chains which can still generate complex — yet specific — trajectories with fewer DOF’s. This paper further extends previous work on the design of such passive-active mechanisms that replicate the natural hand motion along a straight-line. The natural hand motion is described by a smooth bell-shaped velocity profile which in turn is generated by the well-established Minimum-Jerk-Model (MJM). Three different straight line 4-bar linkages, a Chebyshev’s, a Hoeken’s and a Watt’s, are examined. First, with the use of kinetostatic analysis and given the natural hand velocity and acceleration, the torque function of non-linear springs that act on the driving link is deduced. Then, given that the springs are acting, interaction with impaired users is considered and the extra actuation power that can maintain the natural velocity profile is calculated. A multibody dynamics software is employed for further assessing the mechanisms’ dynamic response under varying interaction forces. Also, different parameters like inertia are altered and the effects on internal (springs) and external (actuator) power are examined. Then, the three mechanisms are compared with respect to size, required amount of external power, ergonomic issues etc. Finally, it is investigated whether a linear fit of the non-linear spring torque can be adequate for generating the desired MJM trajectory and operate effectively in collaboration with the active part of the control.