Analysis on the Instantaneous Stiffness of the 3-RPS Parallel Machine

2009 ◽  
Vol 407-408 ◽  
pp. 63-67 ◽  
Author(s):  
Xian Guo Han ◽  
Xue Liang Cui ◽  
Wu Yi Chen
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Parallel Machine ◽  
Force Analysis ◽  
Stiffness Model ◽  
Generalized Force ◽  
Moving Platform ◽  
Position And Orientation

Based on the screw theory, the force analysis of the 3-RPS parallel machine is illuminated. Been equivalent to a 6-chain parallel machine, the deformation harmony equation of the parallel machine under the outside generalized force is interpreted. The instantaneous stiffness model of the parallel machine, which includes the change of the force Jacobian matrix, is established. Considering the deviation of the position and orientation of the moving platform, which is resulted from the distortion of the PRS chains of the parallel machine, the influence of the change of the Jacobian matrix to the instantaneous stiffness model of the 3-RPS parallel machine is analyzed, and furthermore, it is verified with an instance.

Actuating Input Selection of 5-UPS/PRPU Parallel Machine Tool

2005 ◽  
Author(s):  
Jian-She Gao ◽  
Ren-Cheng Zheng ◽  
Yong-Sheng Zhao
Keyword(s):  
Parallel Mechanism ◽  
Basic Problem ◽  
Screw Theory ◽  
Parallel Machine ◽  
Condition Numbers ◽  
Constraint Matrix ◽  
Input Selection ◽  
Moving Platform ◽  
Parallel Machine Tool ◽  
Selection Of

The actuating input selection is an important basic problem for the parallel mechanism. Based on the screw theory, the constraint screw can be got after locking a kinematic pair in any limb, which can be taken as actuating wrench acted on the moving platform of the parallel mechanism. The constraint screw matrix is composed of the structure constraint screws and the constraint screws of the actuating pairs. The reasonableness of input selection can be judged by the rank of the constraint matrix. The performance of the combinations of actuating inputs is evaluated by the condition numbers of the force constraint matrix and the torque constraint matrix respectively. The theory presented is validated by the simulation and the maching test.

Design and Kinematics Analysis of a Novel Planar Parallel Mechanism

2014 ◽  
Vol 568-570 ◽  
pp. 904-910
Author(s):  
Yan Bin Zhang ◽  
Hui Ping Wang
Keyword(s):  
Condition Number ◽  
Parallel Mechanism ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Kinematics Analysis ◽  
Moving Platform ◽  
One To One ◽  
Actuated Joints

A novel 3-dof planar parallel mechanism, which is composed by three different limbs, is designed. The moving platform can translate along two directions and rotate around one axis with respect to the base. Mobility of the mechanism is discussed and calculated based on the screw theory. The forward and the inverse analytical position equations are derived and the veloctiy analysis is addressed too. The Jacobian matrix is an identical one, so there exists one-to-one corresponding linear controlling relationship between one of the actuated joints and one of the outputs of the platform. Moreover, the condition number of the Jacobian matrix is constantly equal to one and the mechanism shows fully-isotropic throughout entire workspace.

Force Analysis of Spatial Single Closed-Loop Overconstrained Mechanisms

2016 ◽  
Author(s):  
Wenlan Liu ◽  
Yundou Xu ◽  
Jiantao Yao ◽  
Yongsheng Zhao
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Driving Forces ◽  
Parallel Mechanisms ◽  
Force Analysis ◽  
Moving Platform ◽  
Compliance Matrices ◽  
Overconstrained Mechanisms ◽  
Force Problem ◽  
Deformation Compatibility

Taking the Bennett and Schatz mechanisms as examples, force analyses of spatial single closed-loop (SSCL) overconstrained mechanisms are demonstrated aiming to obtain the driving forces/torques and joint reactions of this kind of mechanisms. Firstly, regarding the SSCL overconstrained mechanisms as parallel mechanisms with two supporting limbs, the constraint wrenches and actuation wrenches imposed on the moving platform by the two limbs are discussed, and the mobility of each mechanism is analyzed based on the screw theory. Then, the compliance matrices of the limbs’ constraint wrenches are derived, which contribute to solve the statically indeterminate force problem of the mechanisms. Next, by combining the force and moment equilibrium equation of the moving platform with the deformation compatibility equation of the corresponding mechanism, the magnitudes of all constraint wrenches and actuation wrenches are solved. Furthermore, the driving forces/torques and joint reactions are derived. Finally, the numerical and simulation results of the two mechanisms are presented.

Stiffness modelling and comparison of the 5-UPS/PRPU parallel machine tool with its non-redundant counterpart

2016 ◽  
Vol 231 (9) ◽  
pp. 1646-1657 ◽  
Author(s):  
Xin Zhou ◽  
Yundou Xu ◽  
Jiantao Yao ◽  
Kuijing Zheng ◽  
Yongsheng Zhao
Keyword(s):  
Machine Tool ◽  
Stiffness Matrix ◽  
Parallel Mechanism ◽  
Screw Theory ◽  
Virtual Work ◽  
Matrix Decomposition ◽  
Parallel Machine ◽  
Stiffness Model ◽  
Redundantly Actuated ◽  
Parallel Machine Tool

This article presents a derivation of the stiffness matrix of a general redundantly actuated parallel mechanism based on the overall Jacobian. The Jacobian of the constraints and actuations is derived using reciprocal screw theory. Based on the mapping relationship between constraint, actuated and external forces combined with the principle of virtual work, a compatibility equation for the deformation of all of the limbs is achieved, and the stiffness model of the general redundantly actuated parallel mechanism is derived. The 5-UPS/PRPU redundantly actuated parallel machine tool is used to illustrate this method. The parallel machine tool comprehensively reveals the effect of the elastic deformation of active–passive joints and some basic transmission parts. The stiffness model is further validated by experimental data. Moreover, the global stiffness matrix of the general redundantly actuated parallel mechanism can be separated into two parts via matrix decomposition. The first part is the stiffness matrix of the corresponding non-redundant parallel mechanism, and the second part is the stiffness matrix of the redundantly actuated limbs (actuators). The redundantly actuated 5-UPS/PRPU parallel machine tool is also investigated for further analysis. The different stiffness characteristics of the machine tool and its corresponding non-redundant 5-UPS/PRPU parallel machine tool are compared. Actuation redundancy is found to improve the stiffness performance of the machine tool efficiently.

scholarly journals Kinematic analysis of a novel 3-CRU translational parallel mechanism

2015 ◽  
Vol 6 (1) ◽  
pp. 57-64 ◽  
Author(s):  
B. Li ◽  
Y. M. Li ◽  
X. H. Zhao ◽  
W. M. Ge
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Screw Theory ◽  
Structural Characteristics ◽  
Parallel Mechanisms ◽  
Reachable Workspace ◽  
Potential Applications ◽  
Moving Platform ◽  
And Performance

Abstract. In this paper, a modified 3-DOF (degrees of freedom) translational parallel mechanism (TPM) three-CRU (C, R, and U represent the cylindrical, revolute, and universal joints, respectively) structure is proposed. The architecture of the TPM is comprised of a moving platform attached to a base through three CRU jointed serial linkages. The prismatic motions of the cylindrical joints are considered to be actively actuated. Kinematics and performance of the TPM are studied systematically. Firstly, the structural characteristics of the mechanism are described, and then some comparisons are made with the existing 3-CRU parallel mechanisms. Although these two 3-CRU parallel mechanisms are both composed of the same CRU limbs, the types of freedoms are completely different due to the different arrangements of limbs. The DOFs of this TPM are analyzed by means of screw theory. Secondly, both the inverse and forward displacements are derived in closed form, and then these two problems are calculated directly in explicit form. Thereafter, the Jacobian matrix of the mechanism is derived, the performances of the mechanism are evaluated based on the conditioning index, and the performance of a 3-CRU TPM changing with the actuator layout angle is investigated. Thirdly, the workspace of the mechanism is obtained based on the forward position analysis, and the reachable workspace volume is derived when the actuator layout angle is changed. Finally, some conclusions are given and the potential applications of the mechanism are pointed out.

Type Synthesis of Parallel Mechanisms With a Constant Jacobian Matrix

2018 ◽  
Vol 10 (6) ◽  
Author(s):  
Yanzhi Zhao ◽  
Yachao Cao ◽  
Xianwen Kong ◽  
Tieshi Zhao
Keyword(s):  
Jacobian Matrix ◽  
Screw Theory ◽  
Velocity Analysis ◽  
Parallel Mechanisms ◽  
Input Output ◽  
Type Synthesis ◽  
Analysis And Evaluation ◽  
Analysis Design ◽  
Moving Platform ◽  
And Control

Jacobian matrix plays a key role in the analysis, design, and control of robots. For example, it can be used for the performance analysis and evaluation of parallel mechanisms (PMs). However, the Jacobian matrix of a PM generally varies with the poses of the moving platform in the workspace. This leads to a nonconstant performance index of the PM. PMs with a constant Jacobian matrix have simple kinematics and are easy to design and control. This paper proposes a method for obtaining PMs with a constant Jacobian matrix. First, the criteria for detecting invariance of a Jacobian matrix are obtained based on the screw theory. An approach to the synthesis of PMs with a constant Jacobian matrix is then proposed. Using this approach, PMs with a constant Jacobian matrix are synthesized in two steps: the limb design and the combination of the limbs. Several PMs with a constant Jacobian matrix are obtained. In addition to the translational parallel mechanisms (TPMs) with a constant Jacobian matrix in the literature, the mixed-motion PMs whose moving platform can both translate and rotate with a constant Jacobian matrix are newly identified. The input/output velocity analysis of several PMs is presented to verify that Jacobian matrix of these PMs is constant.

Kinematics Simulation of Parallel Mechanism Based on ADAMS

2012 ◽  
Vol 538-541 ◽  
pp. 479-482
Author(s):  
Xin Yu Du ◽  
Hong Wei Liu
Keyword(s):  
Parallel Mechanism ◽  
Screw Theory ◽  
Virtual Prototype ◽  
Degree Of Freedom ◽  
Kinematics Analysis ◽  
Kinematics Simulation ◽  
Spatial Parallel Mechanism ◽  
Moving Platform ◽  
Simulation Results ◽  
Position And Orientation

In this paper,a kind of 3-UPU spatial parallel mechanism is introduced. Through deep analysis of the degree-of-freedom (DoF) for the platform using screw theory， the position and orientation of the moving platform is discussed. At last, the 3D virtual prototype modeling of this 3-UPU parallel mechanism based on software ADAMS is developed; the kinematics simulation and analysis are also carried out accordingly. From the simulation results, we can see that the proposed calculation of the DoFs and kinematics analysis is correct.

Kinematic Performance of 5-UPS/PRPU 5-Axis Parallel Machine Tool

2004 ◽  
Author(s):  
Yong Sheng Zhao ◽  
Kui Jing Zheng ◽  
Qin Chuan Li ◽  
Xiao Jing Tian ◽  
Yan Ming Qin
Keyword(s):  
Machine Tool ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Vertical Axis ◽  
Parallel Machine ◽  
Parameter Method ◽  
Solution Equation ◽  
Axis Parallel ◽  
Moving Platform ◽  
Parallel Machine Tool

A novel 5-UPS/PRPU 5-axis PMT (Parallel Machine Tool) is studied. The stationary platform is connected with the moving platform by the same five UPS actuated limbs and a PRPU passive constraining limb. Three translational DOF (degrees of freedom) and two rotational DOF can be achieved. by using kinematic screw theory and D-H parameter method, the kinematic forward and inverse solutions of the PRPU constraining limb are deduced. The rotational constraint along the vertical axis of the moving platform acted by the PRPU limb is confirmed. Moreover, the configuration of the moving platform can be acquired online by installing sensors on the joints of the constraining limb. The kinematic inverse solution equation and jacobian matrix for this 5-axis PMT are presented. Finally the workspace and the dexterity of the PMT are analyzed. Theoretical analysis is proved by the actual operation of the prototype of the 5-UPS/PRPU 5-axis PMT in our laboratory.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Design and analysis of CICABOT: a novel translational parallel manipulator based on two 5-bar mechanisms

Robotica ◽  
2011 ◽  
Vol 30 (3) ◽  
pp. 449-456 ◽  
Author(s):  
M. F. Ruiz-Torres ◽  
E. Castillo-Castaneda ◽  
J. A. Briones-Leon
Keyword(s):  
Parallel Manipulator ◽  
Jacobian Matrix ◽  
Geometric Analysis ◽  
Vector Equation ◽  
Prismatic Joints ◽  
Hollow Cylinders ◽  
Moving Platform ◽  
Direct Kinematics

SUMMARYThis work presents the CICABOT, a novel 3-DOF translational parallel manipulator (TPM) with large workspace. The manipulator consists of two 5-bar mechanisms connected by two prismatic joints; the moving platform is on the union of these prismatic joints; each 5-bar mechanism has two legs. The mobility of the proposed mechanism, based on Gogu approach, is also presented. The inverse and direct kinematics are solved from geometric analysis. The manipulator's Jacobian is developed from the vector equation of the robot legs; the singularities can be easily derived from Jacobian matrix. The manipulator workspace is determined from analysis of a 5-bar mechanism; the resulting workspace is the intersection of two hollow cylinders that is much larger than other TPM with similar dimensions.

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