A major deficiency of piezoelectric actuators is that their open-loop control accuracy is seriously limited by hysteresis. In this paper, a novel mathematical model is proposed to describe hysteresis precisely and a new parameter called turning voltage is introduced. It was found experimentally that the shapes of hysteresis curves are decided by the value of the turning voltage. A computer-based inverse control approach under open-loop operation based on the mathematical model was applied to suppress the inherent hysteresis to within ±1% full span range of a stack piezoelectric actuator and the performance of the piezoelectric actuator is noticeably improved.

An efficient dynamic modelling approach was presented for planar parallel manipulator with flexible links. To increase the accuracy of the model, an improved curvature-based finite element method (ICFE) was developed for discretisation of the flexible links. Then, a novel approach for analysis of the coupling between rigid-body motion and flexible-body motion was proposed, and compared to the regular geometrical method, the proposed method was accurate and easy to implement. With the aforementioned proposed methods, the Kane equation was integrated to formulate the dynamic model of a 3RRR planar parallel manipulator. Finally, comparison studies were performed to validate the proposed ICFE and the integrated dynamic modelling method. Compared to the regular curvature-based finite element method (CFE), the ICFE exhibits improved accuracy with equivalent degrees of freedom. Additionally, the proposed integrated dynamic model shows a good agreement with the Abaqus model. Therefore, it was concluded that the proposed dynamic modelling method herein was efficient and accurate for parallel manipulators with flexible links, demonstrating reasonable potentials for model based control.

A variable stiffness actuator is inspired by the human motor control and is the most popular actuator used to exploit the human performance and human-like motion. However, these actuators are typically highly non-linear and redundant not only in their kinematics but also in their dynamics due to their capability to modulate their stiffness and positions simultaneously. It is not trivial to generate the trajectory for a strongly non-linear and redundant dynamic system equipped with variable stiffness actuators. In this paper, a trajectory planning method for a variable stiffness actuated robot via a time-energy optimal control policy is proposed. The simulation studies demonstrate the effectiveness of the trajectory planning method through the case studies of a two degree of freedom variable stiffness actuated robot. Furthermore, the results show that the proposed method could be able to generate the motion which is similar to the human arm motion strategy.

To obtain the closed-form forward kinematics of parallel robots, researchers use algebra-based method to transform and simplify the constraint equations. However, this method requires a complicated derivation that leads to high-order univariate variable equations. In fact, some particular mechanisms, such as Delta, or H4 possess many invariant geometric properties during movement. This suggests that one might be able to transform and reduce the problem using geometric approaches. Therefore, a simpler and more efficient solution might be found. Based on this idea, we developed a new geometric approach called geometric forward kinematics (GFK) to obtain the closed-form solutions of H4 forward kinematics in this paper. The result shows that the forward kinematics of H4 yields an eighth degree univariate polynomial, compared with earlier reported 16th degree. Thanks to its clear physical meaning, an intensive discussion about the solutions is presented. Results indicate that a general H4 robot can have up to eight nonrepeated real solutions for its forward kinematics. For a specific configuration of H4, the nonrepeated number of real roots could be restricted to only two, four, or six. Two traveling plate configurations are discussed in this paper as two typical categories of H4. A numerical analysis was also performed for this new method.

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