In order to improve the motion stability of a pointing mechanism, the trajectory planning and trajectory optimization were conducted. To obtain better motion stability, the jerk is required continuous. Therefore, higher order polynomial or B-spline are needed and the calculation amount increases in trajectory planning. A novel hybrid interpolation algorithm “7-order polynomial + improved quartic uniform B-spline curve + 7-order polynomial” was proposed for trajectory planning, which cannot only ensure the trajectory passes through all path points but also ensure the jerk is continuous. From the first path point to the second path point and from the penultimate path point to the last path point, 7-order polynomial is chosen as the interpolation algorithm. The intermediate path points are interpolated by improved quartic uniform B-spline curve which is newly proposed. The improved quartic uniform B-spline curve can pass through all path points and does not require complicated calculation. To carry out the trajectory planning of a X-Y pointing mechanism, the kinematic model was derived at first. Secondly, the hybrid interpolation algorithm was presented. Thirdly, the NSGA-II algorithm was applied to the multi-objective optimization which are time, acceleration and jerk. Finally, the trajectory planning experiment was conducted to prove the validity of the proposed hybrid interpolation algorithm. The experimental results show that the pointing accuracy is improved by using the hybrid interpolation algorithm and the NSGA-II algorithm. This hybrid interpolation algorithm for trajectory planning can be applied to other robots as well.

The lower-mobility parallel mechanism has been widely used in the engineering field due to its numerous excellent characteristics. However, little work has been devoted to the actuator selection and placement that best satisfy the system’s functional requirements during concept design. In this study, a unified approach for synthesizing the actuation spaces of both rigid and flexure parallel mechanisms has been presented, and all possible combinations of inputs could be obtained, laying a theoretical foundation for the subsequent optimization of inputs. According to the linear independence of actuation space and constraint space of the lower-mobility parallel mechanism, a general expression of actuation spaces in the format of screw systems is deduced, a unified synthesis process for the lower-mobility parallel mechanism is derived, and the efficiency of the method is validated with two selective examples based on screw theory. This study presents a theoretical framework for the input selection problems of parallel mechanisms, aiming to help designers select and place actuators in a correct and even optimal way after the configuration design.

In the aerospace field, the precision and stiffness for 2R1T (R denotes the rotation and the T denotes the translation) degree of freedom (DOF) space posture adjustment mechanisms are required. Compliant parallel mechanisms (CPMs) with a suitable constrained branch (SCB) have the advantages of high precision and high stiffness. Based on screw theory, a new type synthesis approach for a 2R1T compliant parallel mechanism with a suitable constrained branch is proposed. The proposed approach is an improvement of the freedom and constraint topology approach. It combines with other methods, including the rigid-body-replacement method, the principle of symmetry, etc. In order to obtain CPMs with a suitable constrained branch, the criterion for the type synthesis is presented. Using this proposed type synthesis approach, a series of CPMs is obtained. They include, but are not limited to, the existing typical 2R1T CPMs with a suitable constrained branch. Furthermore, it identifies the correctness and effectiveness of the approach by analyzing the DOF of the synthesized mechanism. This approach is also suitable for the type synthesis of 4, 5, and 6 DOF compliant parallel mechanisms with a suitable constrained branch.

The contact stiffness of a mechanical bonding surface is an important parameter in determining the normal and radial contact force. To improve the calculation accuracy of the contact force model, the surface roughness of the bonding surface and the energy loss that necessarily occurs during the impact process should be considered comprehensively. To study the normal contact force of a revolute joint with clearance more accurately in the case of dry friction, a nonlinear stiffness coefficient model considering the surface roughness was established based on fractal theory, which considers the elastic, elastic-plastic, and plastic deformations of the asperities of the contact surface during the contact process. On this basis, a modified nonlinear spring damping model was established based on the Lankarani–Nikravesh contact force model. The laws influencing the surface roughness, recovery coefficient, initial velocity, and clearance size on the impact force were revealed, and were compared with the Lankarani–Nikravesh model and a hybrid model using MATLAB. The maximum impact force was obtained using a modified contact force model under different initial velocities, different clearances, and different degrees of surface roughness, and the calculated results were then compared with the experiment results. This study indicates that the modified model can be used more widely than other models, and is suitable for both large and small clearances. In particular, the modified model is more accurate when calculating the contact force of a revolute joint with a small clearance.