Motion-force Transmissibility Characteristic Analysis of a Redundantly Actuated and Overconstrained Parallel Machine

This paper presents a novel 1T2R three degrees of freedom redundantly actuated and overconstrained ■parallel machining head(■denotes the active prismatic joint), which can construct 5-axis hybrid machine to complete high speed freedom surface milling for large complex structural components in aerospace. Firstly, based on the screw theory, the mobility of the proposed parallel manipulator is briefly analysed. Secondly, the kinematic inverse position and the parasitic motion of the parallel manipulator are explicitly expressed. Furthermore, motion-force transmission performance evaluation indices are derived in detail via an alternative approach based on the screw theory. More importantly, a simple method for quickly solving the maximum virtual power coefficient is proposed, and the motion-force transmission performance evaluation index is greatly improved. To evaluate the kinematic performance, its workspace is calculated. With numerical examples, performance distribution atlases of the manipulator are depicted visually. The corresponding results illustrate that the proposed parallel manipulator has better orientation workspace and superior motion-force transmission performance than the 2 PRU-PRS parallel manipulator, which proves the validity and applicability of applying this manipulator as a machining head.

Dynamic Performance Evaluation of a Redundantly Actuated and Over-constrained Parallel Manipulator

This paper presents a redundantly actuated and over-constrained 2 RPU-2 SPR parallel manipulator with two rotational and one translational coupling degrees of freedom.The kinematics analysis is firstly carried out and the mapping relationship of the velocity,acceleration and the independent parameters between the actuator joint and the moving platform are deduced by using the vector dot product and cross product operation.By employing d′Alembert′s principle and the principle of virtual work,the dynamics equilibrium equation is derived,and the simplified dynamics mathematical model of the parallel manipulator is further derived.Simultaneously,the generalized inertia matrix which can characterize the acceleration performance between joint space and operation space is further separated,and the performance indices including the dynamics dexterity,inertia coupling characteristics,energy transmission efficiency and driving force/torque balance are introduced.The analysis results show that the proposed redundantly actuated and over-constrained 2 RPU-2 SPR parallel manipulator in comparison with the existing non-redundant one has better dynamic comprehensive performance,which can be demonstrated practically by the successful application of the parallel kinematic machine head module of the hybrid machine tool.

Variable stiffness design of redundantly actuated planar rotational parallel mechanisms

Redundantly actuated planar rotational parallel mechanisms（RAPRPMs） adapt to the requirements of robots under different working conditions by changing the antagonistic internal force to tune their stiffness.The geometrical parameters of the mechanism impact the performances of modulating stiffness.Analytical expressions relating stiffness and geometrical parameters of the mechanism were formulated to obtain the necessary conditions of variable stiffness.A novel method of variable stiffness design was presented to optimize the geometrical parameters of the mechanism.The stiffness variation with the internal force was maximized.The dynamic change of stiffness with the dynamic location of the mechanism was minimized,and the robustness of stiffness during the motion of the mechanism was ensured.This new approach to variable stiffness design can enable off-line planning of the internal force to avoid the difficulties of on-line control of the internal force.

Type Synthesis and Dynamics Performance Evaluation of a Class of 5-DOF Redundantly Actuated Parallel Mechanisms

This paper presents a five degree of freedom(5-DOF)redundantly actuated parallel mechanism(PM)for the parallel machining head of a machine tool.A 5-DOF single kinematic chain is evolved into a secondary kinematic chain based on Lie group theory and a configuration evolution method.The evolutional chain and four 6-DOF kinematic chain SPS(S represents spherical joint and P represents prismatic joint)or UPS(U represents universal joint)can be combined into four classes of 5-DOF redundantly actuated parallel mechanisms.That SPS-(2UPR)R(R represents revolute joint)redundantly actuated parallel mechanism is selected and is applied to the parallel machining head of the machine tool.All formulas of the 4SPS-(2UPR)R mechanism are deduced.The dynamic model of the mechanism is shown to be correct by Matlab and automatic dynamic analysis of mechanical systems(ADAMS)under no-load conditions.The dynamic performance evaluation indexes including energy transmission efficiency and acceleration performance evaluation are analyzed.The results show that the 4SPS-(2UPR)R mechanism can be applied to a parallel machining head and have good dynamic performance.

Methods for Force Analysis of Overconstrained Parallel Mechanisms： A Review

The force analysis of overconstrained PMs is relatively complex and difficult, for which the methods have always been a research hotspot. However, few liter- atures analyze the characteristics and application scopes of the various methods, which is not convenient for researchers and engineers to master and adopt them prop- erly. A review of the methods for force analysis of both passive and active overconstrained PMs is presented. The existing force analysis methods for these two kinds of overconstrained PMs are classified according to their main ideas. Each category is briefly demonstrated and evaluated from such aspects as the calculation amount, the compre- hensiveness of considering limbs＇ deformation, and the existence of explicit expressions of the solutions, which provides an important reference for researchers and engi- neers to quickly find a suitable method. The similarities and differences between the statically indeterminate prob- lem of passive overconstrained PMs and that of active overconstrained PMs are discussed, and a universal method for these two kinds of overconstrained PMs is pointed out. The existing deficiencies and development directions of the force analysis methods for overconstrained systems are indicated based on the overview.

Stability Analysis for a Planar Parallel Manipulator with the Capability of Self-Coordinating the Load Distribution

Redundantly actuated parallel manipulators have the advantage of enhancing load-carrying capability over their non-redundant ones, however they also cause the problem of uneven load distribution and need a high requirement for the control system. This paper presents a 2-RPR/RP planar redundantly actuated parallel manipulator which can self-coordinate the distribution of external loads. This capability is realized by an appropriate design of the moving platform to make the manipulator stable at equilibrium position. The stability is proved by the theorem of direct Lyapunov method in classical mechanics. The numerical simulations are conducted to validate the stable capability by means of the observation of potential energies and phase planes. This paper offers an alternative way to design a redundantly actuated manipulator with the capability of self-coordinating the load distribution to actuations, such that parts of the controlling work are assigned to the manipulator itself by its own structure and only a little work remains to the control system.