Modified Shadow Robot Control method for optimal path synthesis of mechanisms: Application to five-link mechanism

Abstract

For optimal path synthesis of a mechanism with a single degree of freedom (DOF), a powerful method called Shadow Robot Control (SRC) has been recently proposed in the literature. However, this method is restricted to synthesis problems with prescribed timing (i.e. problems in which a particular input crank angle is associated with each point of the desired trajectory). In this paper, the SRC method was elaborated and modified to be capable of synthesizing both prescribed and nonprescribed timing problems. For this purpose, a new structure of contour error and objective function estimation was presented. As a result, there is no need to consider the input angles (crank angles) corresponding to desired path points as optimization parameters, even for non-prescribed timing problems. This prevents unnecessarily enlarging the search space, providing a more effective and robust optimization method (with respect to initial guess). The synthesis of a geared five-link mechanism was used to detail the proposed algorithm as a case study. Despite the five-link mechanism capability and simplicity of generating a complicated trajectory, this single DOF path generator seems less investigated in the literature. Few existing numerical problems of the five-link mechanism in the literature were solved. The comparison of the results shows the effective performance of the proposed algorithm in synthesizing the mechanism.

Design of a novel low-speed gait rehabilitation device incorporating a synthesized geared five-bar mechanism

“…The five-bar mechanism has two DOFs by default unless a belt-pulley train or gear set is used to confine two crank link rotations to each other, as illustrated in Figure 4. 43 Thus, the obtained geared five-bar mechanism has a single DOF.…”

“…This study employs a geared five-bar mechanism for gait rehabilitation due to its exceptional capabilities and adjustability to generate complex trajectories. 43 The mechanism's dimensions must be synthesized and adjusted to achieve this objective.…”

“…The step tolerance and maximum number of iterations of the local solver are set to their default values. 43 Optimal dimensions obtained using the SRC method and applying the global optimization algorithm are listed in Table 1.…”

“…where T v is the PD controller’s time derivative constant and e c is the contour error between the generated and desired trajectories. By substituting the control signal relationship of (6) with that of (5), the objective function is simplified 31,43 :…”

“…Also, it has fewer links and is less bulky compared to six-bar and eight-bar types of single-DOF mechanisms. 43,44 Also, it is simpler, lighter, and easier to manufacture and maintain compared to other mechanisms with one DOF having more links. It has less potential for friction, making it faster, easier to control and maneuver, and simpler to understand and troubleshoot.…”