Analysis of kinematic and singular configurations of an asymmetrical parallel mechanism

The forward kinematics and singularity configuration of an asymmetrical parallel mechanism with three translational degrees of freedom were analyzed. By establishing the position equations of the mechanism and obtaining the forward solutions, a better decoupling of the mechanism was proved. Based on the Jacobi velocity transfer matrix, the possible singularity configurations were studied and the methods avoiding these configurations discussed. Although improving the rigidity, the 4R structures in the mechanism also resulted in new singularity configurations. By analysis of a feasible instance, this kind of parallel mechanism can avoid all singularity configurations. Meanwhile, it was proved that the design of structure parameters and the choice of inputs range are important for rigidity and stability of parallel mechanisms.

STUDY ON SINGULAR CONFIGURATIONS AND COMPUTER SIMULATION OF 6R ROBOT

When robot is at singular configuration, the limited hand velocity wouldrequire some joints with infeasible speeds so as to lead unsafely of the system. A method of solvingthe approximate velocity of joint near singular configuration point by adding damped vector isproposed and a modified algorithm is provided. With the analysis of J^(-1) the singularconfigurations of 6R robot are divided into structure boundary singularity , boundary singularity ,inner singularity and wrist singularity. The conditions of singularities of the robot have beenascertained. The computer simulations of the singularities of the robot are developed, which havemany advantages over previous description methods of the singular configurations of robot. With thehelp of boundary singularity analysis, a application in welding trajectory planning checking of therobot has been carried out and the simulation result proved visualized and useful.

Singular Assembly Configurations and Configuration Bifurcation Characteristics of the Semi-regular Hexagons 6-6 Gough-Stewart Manipulator

It is well known that singular configurations are inherent to parallel manipulators and have serious influences on their properties. Therefore, these singular configurations should be avoided in the design and application of mechanisms. The researches on the singularity identification and distribution have revealed the relations among the six configuration parameters at singular points. Few works have dealt with the relation between the singularity and the input parameters, as wcll as the properties of the manipulator nearby the singularity. In this paper, taking the semi-regular hexagons 6-6 Gough-Stewart manipulator （SRHGSMP） as an example, the configuration bifurcation characteristics going with the input parameters, the assembly configurations at singular points, and the reasons to cause the singularity are analyzed. The research reveals that the number and the combination of the input parameters have great influences on the complexity of the singularity and the curvature radiuses of the configuration curves. Under different number of input parameters, the dimensional-utmost singularity, line vectors correlation singularity and Jacobian matrix correlation singularity can occur individually or jointly. Choosing the adjacent input parameters, the simple singularity and the large singularity-free input parameters zones can be obtained. And selecting multiple input parameters, the self-motion regions and the singularity avoidance errors can be reduced. These new discoveries are valuable and of significance for the trajectory design, the singularity avoidance, and the self-motion control of the parallel manipulator.

STUDY OF REGULARITY OF GENERAL-LINEAR-COMPLEX SINGULARITY OF 3/6-STEWART MECHANISM

The general-linear-complex singularity of Stewart mechanism is a veryimportant problem in the parallel manipulator. Its general regularity is not found yet during thepast two decades. St-Onge and Gosselin pointed Out that the singularity locus of the Stewartmechanism at some given orientations of the moving platform should be polynomial expressions withvaried degrees in 2000, but they didn't formulate the expression. Based on the kinematicssingularity principle and the geometry condition proposed by Huang Zhen in 1999, firstly thesingularity equation in degree two is derived. It is a hyperbola when the orientation of the movingplatform is given. This result is also proved using screw theory. Then some singularity surfaces aregotten in three-dimensional space. This result is of important significance.

Spacecraft attitude maneuver control using two parallel mounted 3-DOF spherical actuators

A parallel configuration using two 3-degree-of-freedom（3-DOF） spherical electromagnetic momentum exchange actuators is investigated for large angle spacecraft attitude maneuvers.First, the full dynamic equations of motion for the spacecraft system are derived by the NewtonEuler method. To facilitate computation, virtual gimbal coordinate frames are established. Second,a nonlinear control law in terms of quaternions is developed via backstepping method. The proposed control law compensates the coupling torques arising from the spacecraft rotation, and is robust against the external disturbances. Then, the singularity problem is analyzed. To avoid singularities, a modified weighed Moore-Pseudo inverse velocity steering law based on null motion is proposed. The weighted matrices are carefully designed to switch the actuators and redistribute the control torques. The null motion is used to reorient the rotor away from the tilt angle saturation state. Finally, numerical simulations of rest-to-rest maneuvers are performed to validate the effectiveness of the proposed method.