A survey of instantaneous poles for a class of two-degree-of- freedom spherical mechanisms

This paper is a detailed exploration of instantaneous poles for a class of two-degree-of-freedom （two-DOF） spherical mechanisms （SMs） with seven links or bars. For two-DOF SMs, the secondary instantaneous poles （the ones which cannot be found by direct inspection） must lie on the specified great circles. For many of these mechanisms, however, some of these great circles cannot be obtained by a direct application of Aronhold-Kennedy theorem. This paper presents geome- trical and analytical techniques to locate these unknown great circles for three topologies of seven-bar two-DOF SMs.

On the location of the secondary instantaneous poles in two-degree-of-freedom spherical mechanisms

As the instant centers in planar mechanisms, the instantaneous poles （or instant poles, in brief） can be used for kinematic analysis in spherical mechanisms. One of the mandatory steps in this analysis is the determination of the location of these poles. This paper presents a theorem showing analytically that the locus of an unknown secondary instant pole in two-degree-of-freedom （2-DOF） spherical mechanisms is a great circle （GC）. The exact location of the pole on its GC is obtained based on the configuration of the mechanism and velocity ratio of the two inputs. Moreover, using the results of the theorem, a geometrical technique is presented to determine the GC of the pole.

DYNAMICS ANALYSIS OF 2-DOF SPHERICAL PARALLEL MECHANISM

The analytical formulations of the velocity and the acceleration of a 2-DOF spherical parallel mechanism are derived by the screw theory. Based on building its dynamics model by the principle of virtual work and reciprocal product of the screw, the equation of the motor moment is obtained. Through the transformation of dynamics model, the configuration space method of the dynamics equation and the corresponding coefficients are presented. Finally, the result of an example shows that the inertia moment and the gravity play a more important role than the coriolis and centrifugal moment, and the former is ten times of the latter in the magnitude. So, the latter can be neglected only when the velocity of mechanism is very slow.

Biomimetic Shoulder Complex Based on 3-PSS/S Spherical Parallel Mechanism

The application of the parallel mechanism is still limited in the humanoid robot fields, and the existing parallel humanoid robot joint has not yet been reflected the characteristics of the parallel mechanism completely, also failed to solve the problem, such as small workspace, effectively. From the structural and functional bionic point of view, a three degrees of freedom（DOFs） spherical parallel mechanism for the shoulder complex of the humanoid robot is presented. According to the structure and kinetic characteristics analysis of the human shoulder complex, 3-PSS/S（P for prismatic pair, S for spherical pair） is chosen as the original configuration for the shouder complex. Using genetic algorithm, the optimization of the 3-PSS/S spherical parallel mechanism is performed, and the orientation workspace of the prototype mechanism is enlarged obviously. Combining the practical structure characteristics of the human shouder complex, an offset output mode, which means the output rod of the mechanism turn to any direction at the point a certain distance from the rotation center of the mechanism, is put forward, which provide possibility for the consistent of the workspace of the mechanism and the actual motion space of the human body shoulder joint. The relationship of the attitude angles between different coordinate system is derived, which establishs the foundation for the motion descriptions under different conditions and control development. The 3-PSS/S spherical parallel mechanism is proposed for the shoulder complex, and the consistence of the workspace of the mechanism and the human shoulder complex is realized by the stuctural parameter optimization and the offset output design.

MECHANISM DESIGN AND MOTION ANALYSIS OF A SPHERICAL MOBILE ROBOT

A new spherical mobile robot BHQ-1 is designed. The spherical robot is driven by two internally mounted motors that induce the ball to move straight and turn around on a fiat surface. A dynamic model of the robot is developed with Lagrange method and factors affecting the driving torque of two motors are analyzed. The relationship between the turning radius of the robot and the length of two links is discussed in order to optimize its mechanism design. Simulation and experimental results demonstrate the good controllability and motion performance of BHQ-1.

Kinematic Solution of Spherical Stephenson-Ⅲ Six-bar Mechanism

A closed-form solution can be obtained for kinematic analysis of spatial mechanisms by using analytical method.However,extra solutions would occur when solving the constraint equations of mechanism kinematics unless the constraint equations are established with a proper method and the solving approach is appropriate.In order to obtain a kinematic solution of the spherical Stephenson-III six-bar mechanism,spherical analytical theory is employed to construct the constraint equations.Firstly,the mechanism is divided into a four-bar loop and a two-bar unit.On the basis of the decomposition,vectors of the mechanism nodes are derived according to spherical analytical theory and the principle of coordinate transformation.Secondly,the structural constraint equations are constructed by applying cosine formula of spherical triangles to the top platform of the mechanism.Thirdly,the constraint equations are solved by using Bezout’ s elimination method for forward analysis and Sylvester’ s resultant elimination method for inverse kinematics respectively.By the aid of computer symbolic systems,Mathematica and Maple,symbolic closed-form solution of forward and inverse displacement analysis of spherical Stephenson-III six-bar mechanism are obtained.Finally,numerical examples of forward and inverse analysis are presented to illustrate the proposed approach.The results indicate that the constraint equations established with the proposed method are much simpler than those reported by previous literature,and can be readily eliminated and solved.

Motion Characteristics Analysis of a Novel Spherical Two-degree-of-freedom Parallel Mechanism

Current research on spherical parallel mechanisms(SPMs)mainly focus on surgical robots,exoskeleton robots,entertainment equipment,and other fields.However,compared with the SPM,the structure types and research contents of the SPM are not abundant enough.In this paper,a novel two-degree-of-freedom(2DOF)SPM with symmetrical structure is proposed and analyzed.First,the models of forward kinematics and inverse kinematics are established based on D-H parameters,and the Jacobian matrix of the mechanism is obtained and verified.Second,the workspace of the mechanism is obtained according to inverse kinematics and link interference conditions.Next,rotational characteristics analysis shows that the end effector can achieve continuous rotation about an axis located in the mid-plane and passing through the rotation center of the mechanism.Moreover,the rotational characteristics of the mechanism are proved,and motion planning is carried out.A numerical example is given to verify the kinematics analysis and motion planning.Finally,some variant mechanisms can be synthesized.This work lays the foundation for the motion control and practical application of this 2DOF SPM.

Stiffness Analysis of Spherical Parallel Mechanism U_(P+R) with 2-DOF

As one of the typical less-mobility parallel mechanisms, the spherical parallel mechanism Up.s with two degrees of freedom （2-DOF） possess high order overconstraints, and the calculation of its stiffness is partly different with general parallel mechanisms owing to the bars in each branch are assumed to be arc-shaped. By means of small deformation superposition principle, the relationship between the angle displacement and line displacement of moving platform and the forces acted on the branches were derived out. Based on the results of static analysis, the relationship between the applied force, the line displacement and the angle displacement of the mechanism was set up. And then the stiffness matrix was obtained. The six principal stiffness of the mechanism and the corresponding directions were achieved by the orthogonal transformation. The numerical calculation was performed and the results showed that the principal stiffness and directions are varied with the pose-position of the mechanism, and the principal stiffness is gradually enlarged when it is far away from the anigin. In addition, the torsion stiffness is much greater and the line deformation stiffness is smaller, the difference between the two parts is huge. The research content of this paper supplies the theoretical foundation for the further engineering design and application of the spherical parallel mechanism.

SINGULARITIES OF SPHERICAL FOUR-BAR MOTION

The link curve of a spherical four bar mechanism can be separated into two branches. The condition that the double points of the curve must satisfy is given. The double points may be the double points of either branch, or the intersection points of the two branches.

Mechanics Unloading Analysis and Experimentation of a New Type of Parallel Biomimetic Shoulder Complex

The structure design for high ratio of carrying capacity to deadweight is one of the challenges for the bionic mechanism,while the problem concerning high carrying capacity has not yet be solved for the existing shoulder complex.A new type biomimetic shoulder complex,which adopts 3-PSS/S（P for prismatic pair,S for spherical pair） spherical parallel mechanism（SPM）,is proposed.The static equilibrium equations of each component are established by using the vector method and the equations for constrain forces with certain load are solved.Then the constrain force on the middle limb and that on the side limbs are compared in order to verify the unloading performance of the mechanism.In addition,the prototype mechanism of the shoulder complex is developed,and the force feedback experiment is conducted to verify the static analysis,which indicates that the middle limb suffers most of the external force and the effect of mechanics unloading is achieved.The 3-PSS/S spherical parallel mechanism is presented for the shoulder complex,and the realization of mechanics unloading is benefit for the improvement of the carrying capacity of the shoulder complex.