The complexity of the kinematics and dynamics of a manipulator makes it necessary to simplify the modeling process. However, the traditional representations cannot achieve this because of the absence of coordinate invariance. Therefore, the coordinate invariant method is an important research issue. First, the rigid-body acceleration, the time derivative of the twist, is proved to be a screw, and its physical meaning is explained. Based on the twist and the rigid-body acceleration, the acceleration of the end-effector is expressed as a linear-bilinear form, and the kinematics Hessian matrix of the manipulator(represented by Lie bracket) is deduced. Further, Newton-Euler’s equation is rewritten as a linear-bilinear form, from which the dynamics Hessian matrix of a rigid body is obtained. The formulae and the dynamics Hessian matrix are proved to be coordinate invariant. Referring to the principle of virtual work, the dynamics Hessian matrix of the parallel manipulator is gotten and the detailed dynamic model is derived. An index of dynamical coupling based on dynamics Hessian matrix is presented. In the end, a foldable parallel manipulator is taken as an example to validate the deduced kinematics and dynamics formulae. The screw theory based method can simplify the kinematics and dynamics of a manipulator, also the corresponding dynamics Hessian matrix can be used to evaluate the dynamical coupling of a manipulator.

Nowadays improving the accuracy and enlarging the measuring range of six-axis force sensors for wider applications in aircraft landing, rocket thrust, and spacecraft docking testing experiments has become an urgent objective. However, it is still difficult to achieve high accuracy and large measuring range with traditional parallel six-axis force sensors due to the influence of the gap and friction of the joints. Therefore, to overcome the mentioned limitations, this paper proposed a 6-Universal-Prismatic-Universal-Revolute (UPUR) joints parallel mechanism with flexible joints to develop a large measurement range six-axis force sensor. The structural characteristics of the sensor are analyzed in comparison with traditional parallel sensor based on the Stewart platform. The force transfer relation of the sensor is deduced, and the force Jacobian matrix is obtained using screw theory in two cases of the ideal state and the state of flexibility of each flexible joint is considered. The prototype and loading calibration system are designed and developed. The K value method and least squares method are used to process experimental data, and in errors of kind Ι and kind II linearity are obtained. The experimental results show that the calibration error of the K value method is more than 13.4%, and the calibration error of the least squares method is 2.67%. The experimental results prove the feasibility of the sensor and the correctness of the theoretical analysis which are expected to be adopted in practical applications.

SUMMARY: This paper investigates a 6-degree-of-freedom foldable parallel mechanism for the ship-based stabilized platform, which is driven by closed chain linkages. The velocity and acceleration mappings between the moving platform and inputs of the closed chain linkages are deduced in the form of the first- and second-order influence coefficient matrices. The continuous stiffness matrix is deduced; furthermore, the translation and rotational stiffness along any direction are also deduced. With directional stiffness, the singularity of the mechanism is analyzed, and the explanation of the singularity is given from the viewpoint of stiffness. The directions the platform cannot move or lose its constraints are got from directional stiffness.

This article presents a coupling 3-PSR/PSU parallel mechanism for ship-based stabilized platform based on the coupling characteristics of the ship motions. With coupling characteristics, the goal of 3-axis drives and 5-axis compensation of the moving platform is achieved. From the screw theory, degrees-of-freedom and coupling kinematic characteristics of the mechanism are analyzed. A method for equivalent transformation of motion parameters is proposed. This presents a mapping relationship between the independent degrees-of-freedom and the coupling degrees-of-freedom. The investigations are further extended to the coupling dynamics characteristics of the mechanism. In particular, the effects produced by the coupling force/torque to the system are analyzed. Hence, taking minimum system driving force as the optimization goal, the coupling dynamic equation of the parallel mechanism is established. The numerical example reveals that this coupling parallel mechanism can be applied to the multi-axis compensation of ship-based stabilized platform. The study also enriches the application area of lower-mobility parallel mechanism.

With the increasing demand for the attitude adjustment and vibration isolation of the precision instruments, this paper proposes a three-degrees-of-freedom hybrid-drive parallel mechanism and carries out the kinematic analysis and dimensional synthesis for it. First, the advantages of the hybrid-drive unit are introduced by comparison with the common driving methods. Then, the degrees of freedom of the hybrid-drive parallel mechanism is analyzed by constrained screw method, and the displacement mapping relationship between the generalized input and the moving platform is obtained by a successive approximation iteration method. Furthermore, the first-order and the second-order influence coefficients of the hybrid-drive mechanism are established on the basis of screw theory and the direct method. Besides, the operational dexterity index, the transfer performance index and the stiffness performance index of the hybrid-drive mechanism are introduced, and each single-objective dimensional synthesis of the hybrid-drive mechanism is carried out by the interior point method. Moreover, the multi-objective dimensional synthesis of the hybrid-drive mechanism is proposed by combining the genetic algorithm and the Pareto-optimal solution. Finally, taking the integer numbers of No.23 Pareto set as the numerical example, the kinematics formulas of the hybrid-drive mechanism are verified by the simulation and the experiment.