Theory of Degrees of Freedom for Parallel Mechanisms with Three Spherical Joints and Its Applications

The analysis of degrees of freedom（DOF） of a moving platform is the fundamental problem in kinematics of parallel mechanism. However, many problems should be considered to correctly perform the DOF calculation by using the traditional DOF criterion, and it is difficult to find a DOF criterion suitable for all kinds of mechanisms. A rule that can be used to determine the position and orientation of the moving platform is presented. Based on the proposed rule, a new form of DOF criterion is proposed, which is suitable for a class of parallel mechanisms with three spherical joints attached to the moving platform. The basic types of generalized limb structures are given based on the possible dimension of achieving the center of spherical joint attached to the moving platform, and the general steps of analyzing the DOF are presented. This proposed formula simplifies the DOF analysis of parallel mechanisms with spherical joints attached to the moving platform, and plays an important role in structural synthesis of such parallel mechanisms.

Static Force-Based Modeling and Parameter Estimation for a Deformable Link Composed of Passive Spherical Joints With Preload Forces

To balance the contradiction between higher flexibility and heavier load bearing capacity,we present a novel deformable manipulator which is composed of active rigid joints and deformable links.The deformable link is composed of passive spherical joints with preload forces between socket-ball surfaces.To estimate the load bearing capacity of a deformable link,we present a static force-based model of spherical joint with preload force and analyze the static force propagation in the deformable link.This yields an important result that the load bearing capacity of a spherical joint only depends on its radius,preload force,and static friction coefficient.We further develop a parameter estimation method to estimate the product of preload force and static friction coefficient.The experimental results validate our model.80.4%of percentage errors on the maximum payload mass prediction are below 15%.

Experiments on Large-Diameter Welded Hollow Spherical Joint

We experimented on welded hollow spherical joint of a stadium steel roof to investigate the stress and strain distributions on the surface of the joint and determine the ultimate bearing capacity. Then, finite element analysis was made to experimental results. When the test load was 140% of the design load, the stress at the bottom of the fourth wimble pipe reached the yield point. The experimental results agree with the analytical results well.

Dynamic Modeling and Analysis of 4UPS-UPU Spatial Parallel Mechanism with Spherical Clearance Joint

Clearance between the moving joints is unavoidable in real working process. At present, many researches are mainly focused on dynamics of plane revolute joint in plane mechanism, but few on dynamics of spatial spherical joint clearance in spatial parallel mechanism. In this paper, a general method is proposed for establishing dynamic equations of spatial parallel mechanism with spatial spherical clearance by Lagrange multiplier method. The kinematic model and contact force model of the spherical joint clearance were established successively. Lagrange multiplier method was used to deduce the dynamics equation of 4 UPS-UPU mechanism with spherical clearance joint systematically. The influence of friction coefficient on dynamics response of 4 UPS-UPU mechanism with spherical clearance joint was analyzed. Non-linear characteristics of clearance joint and moving platform were analyzed by Poincare map, phase diagram, and bifurcation diagram. The results show that variation of friction coefficient and clearance value had little effect on stability of the mechanism, but the chaotic phenomenon was found at spherical clearance joint. The research has theoretical guiding significance for improving the dynamic performance and avoiding of chaos of parallel mechanisms including spherical joint clearance.

Design and Strength Analysis of A Spherical Connector for Lifting Subsystem in Deep Sea Mining System

A flexible connector of lifting pipes in a deep sea mining system is designed. The buttress thread （ based on API standard） is used and foreign experience in connector design is referred to. With this kind of connector, the lifting pipe wiU only bear the axial force, free of moment. The strength of the connector is analyzed in detail, including the connecting strength of the buttress thread, the dynamic load of the pipe system, pressures inside and outside of the pipe, the lateral stress of the pipe wall and so on. Especially, a geometric model is built for 3-D contact stress analysis. The distribution graph of contact stress is presented. It is indicated that the strength of the spherical connector meets the demand.

Numerical Modeling of a Spar Platform Tethered by a Mooring Cable

Virtual simulation is an economical and efficient method in mechanical system design. Numerical modeling of a spar platform, tethered by a mooring cable with a spherical joint is developed for the dynamic simulation of the floating structure in ocean. The geometry modeling of the spar is created using finite element methods. The submerged part of the spar bears the buoyancy, hydrodynamic drag force, and effect of the added mass and Froude-Krylov force. Strip theory is used to sum up the forces acting on the elements. The geometry modeling of the cable is established based on the lumped-mass-and-spring modeling through which the cable is divided into 10 elements. A new element-fixed local frame is used, which is created by the element orientation vector and relative velocity of the fluid, to express the loads acting on the cable. The bottom of the cable is fixed on the seabed by spring forces, while the top of the cable is connected to the bottom of the spar platform by a modified spherical joint. This system suffers the propagating wave and current in the X-direction and the linear wave theory is applied for setting of the propagating wave. Based on the numerical modeling, the displacement-load relationships are analyzed, and the simulation results of the numerical modeling are compared with those by the commercial simulation code, Proteus DS. The comparison indicates that the numerical modeling of the spar platform tethered by a mooring cable is well developed, which provides an instruction for the optimization of a floating structure tethered by a mooring cable system.