A Method to Evaluate and Calculate the Mobility of a General Compliant Parallel Manipulator

2004 ◽  
Author(s):  
Jingjun Yu ◽  
Shusheng Bi ◽  
Guanghua Zong
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Parallel Manipulators ◽  
Kinematic Characteristic ◽  
Parallel Kinematic Machine ◽  
Compliance Matrix ◽  
Multiple Degrees Of Freedom ◽  
Parallel Kinematic

A compliant parallel manipulator (CPM), is a kind of compliant mechanism characterizes a complicate topological structure and multiple degrees of freedom. As one of the kinematic characteristics of a CPM, the mobility of a CPM become complicate compared to its rigid-counterpart. In order to describe such a complicate kinematic characteristic of a CPM, “primary mobility of a compliant parallel manipulator” concept is proposed. By means of the screw theory, a method of quantifying the primary mobility of the CPM is investigated under the ground that the compliance matrix of the manipulator should be calculated primarily. By using this method, the primary mobility of two typical compliant parallel manipulators, one is a planar 3-RRR CPM and the other a spatial 3-RRPR CPM, is addressed respectively. This proposed method is also instructive for analyzing the instantaneous mobility of a general degenerate-DOF parallel manipulator or a Parallel Kinematic Machine (PKM).

A 2(3-RRPS) parallel manipulator inspired by Gough–Stewart platform

Robotica ◽  
2012 ◽  
Vol 31 (3) ◽  
pp. 381-388 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Mario A. García-Murillo ◽  
Eduardo Castillo-Castaneda
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Triangular Prism ◽  
Input Output ◽  
Six Degrees Of Freedom ◽  
Moving Platform

SUMMARYThis study addresses the kinematics of a six-degrees-of-freedom parallel manipulator whose moving platform is a regular triangular prism. The moving and fixed platforms are connected to each other by means of two identical parallel manipulators. Simple forward kinematics and reduced singular regions are the main benefits offered by the proposed parallel manipulator. The Input–Output equations of velocity and acceleration are systematically obtained by resorting to reciprocal-screw theory. A case study, which is verified with the aid of commercially available software, is included with the purpose to exemplify the application of the method of kinematic analysis.

scholarly journals Design of Four-DoF Compliant Parallel Manipulators Considering Maximum Kinematic Decoupling for Fast Steering Mirrors

Actuators ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 292
Author(s):  
Guangbo Hao ◽  
Haiyang Li ◽  
Yu-Hao Chang ◽  
Chien-Sheng Liu
Keyword(s):  
Degrees Of Freedom ◽  
Compliant Mechanism ◽  
Parallel Manipulators ◽  
Laser Beams ◽  
Element Analysis ◽  
Compliance Matrix ◽  
Precision Control ◽  
Motion System ◽  
Matrix Modelling

Laser beams can fluctuate in four directions, which requires active compensation by a fast steering mirror (FSM) motion system. This paper deals with the design of four-degrees-of-freedom (DoF) compliant parallel manipulators, for responding to the requirements of the FSM. In order to simplify high-precision control in parallel manipulators, maximum kinematic decoupling is always desired. A constraint map method is used to propose the four required DoF with the consideration of maximum kinematic decoupling. A specific compliant mechanism is presented based on the constraint map, and its kinematics is estimated analytically. Finite element analysis demonstrates the desired qualitative motion and provides some initial quantitative analysis. A normalization-based compliance matrix is finally derived to verify and demonstrate the mobility of the system clearly. In a case study, the results of normalization-based compliance matrix modelling show that the diagonal entries corresponding to the four DoF directions are about 10 times larger than those corresponding to the two-constraint directions, validating the desired mobility.

Motion Plan of a Parallel Kinematic Machine Based on Stiffness Control

2010 ◽  
Author(s):  
Zhongzhe Chi ◽  
Dan Zhang ◽  
Qiaokang Liang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Tool Path ◽  
Parallel Kinematic Machine ◽  
Tool Path Planning ◽  
Parallel Kinematic ◽  
Stiffness Control ◽  
Three Degrees Of Freedom

This paper proposes a design for a machine tool based on a parallel kinematic manipulator with three degrees of freedom, including rotations about x and y axis and translation along z axe. Based on the investigated displacement and inverse kinematics, the system stiffness of the parallel manipulator is conducted. Then in order to observe the highest system stiffness single and multi objective optimizations are performed in terms of rotation angles about x and y axis and translation displacement along z axe. Finally, a case study of tool path planning is presented to demonstrate the application of stiffness mapping.

A Study of the Mobility of a Family of 3-DOF Parallel Manipulators via Screw Theory

2009 ◽  
Author(s):  
Ernesto Rodriguez-Leal ◽  
Jian S. Dai ◽  
Gordon R. Pennock
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators

This paper investigates the mobility of a family of 3-DOF parallel manipulators using screw theory. Based on the 3-PSP, 3-PPS and 3-PCU manipulators and a new 3-CUP parallel manipulator, the paper obtains the branch motion-screws for these architectures and determines the sets of platform constraint-screws. The constraints are identified to be the forces acting on the S and U joints fixed in the platform and the couples acting about an axis perpendicular to the base. The mobility of a manipulator platform is thus obtained by determining the reciprocal screws to the platform constraint screw sets and the platforms are identified to have three instantaneous independent degrees of freedom which are: (i) a translation along an axis perpendicular to the base; and (ii) two rotations about two skew axes.

Kinematics analysis of a redundantly actuated 4-RUU translational parallel manipulator and its nonredundant 3-RUU counterpart

2016 ◽  
Vol 231 (17) ◽  
pp. 3238-3249 ◽  
Author(s):  
Haibo Qu ◽  
Sheng Guo ◽  
Ying Zhang
Keyword(s):  
Comparative Study ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Kinematics Analysis ◽  
Universal Joint ◽  
Torque Distribution ◽  
Redundantly Actuated

This paper presents a comparative study of the kinematics and torque distribution performance of a nonredundant 3-RUU and a redundantly actuated 4-RUU (R: revolute joint, U: universal joint) translational parallel manipulators. First, the reason for unexpected rotations is analyzed based on screw theory and a redundantly actuated 4-RUU translational parallel manipulator is presented to eliminate the unexpected rotations. Then, the degrees of freedom, inverse kinematics, Jacobian matrices, and workspace of 3-RUU and 4-RUU parallel manipulators are analyzed. Finally, a comparative study of torque distribution is performed. The results show that the redundantly actuated 4-RUU parallel manipulator can overcome the unexpected rotations and possesses an improved torque distribution, compared with the nonredundant 3-RUU parallel manipulator.

Determination of the Workspace of a Three-Degrees-of-Freedom Parallel Manipulator Using a Three-Dimensional Computer-Aided-Design Software Package and the Concept of Virtual Chains1

2015 ◽  
Vol 8 (2) ◽  
Author(s):  
Andrew Johnson ◽  
Xianwen Kong ◽  
James Ritchie
Keyword(s):  
Computer Aided Design ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Graphical Representation ◽  
Three Dimensional ◽  
Parallel Manipulators ◽  
Workspace Analysis ◽  
Computer Aided ◽  
Aided Design

The determination of workspace is an essential step in the development of parallel manipulators. By extending the virtual-chain (VC) approach to the type synthesis of parallel manipulators, this technical brief proposes a VC approach to the workspace analysis of parallel manipulators. This method is first outlined before being illustrated by the production of a three-dimensional (3D) computer-aided-design (CAD) model of a 3-RPS parallel manipulator and evaluating it for the workspace of the manipulator. Here, R, P and S denote revolute, prismatic and spherical joints respectively. The VC represents the motion capability of moving platform of a manipulator and is shown to be very useful in the production of a graphical representation of the workspace. Using this approach, the link interferences and certain transmission indices can be easily taken into consideration in determining the workspace of a parallel manipulator.

Structure Synthesis of 3-RRS Type Spatial Compliant Parallel Manipulator

2010 ◽  
Vol 44-47 ◽  
pp. 1375-1379
Author(s):  
Da Chang Zhu ◽  
Li Meng ◽  
Tao Jiang
Keyword(s):  
Parallel Manipulator ◽  
Compliant Mechanisms ◽  
Screw Theory ◽  
Weight Ratio ◽  
Parallel Manipulators ◽  
Robot System ◽  
New Approach ◽  
Structure Synthesis ◽  
Rigid Joints ◽  
Type 3

Parallel manipulators has been extensively studied by virtues or its high force-to-weight ratio and widely spread applications such as vehicle or flight simulator, a machine tool and the end effector of robot system. However, as each limb includes several rigid joints, assembling error is demanded strictly, especially in precision measurement and micro-electronics. On the other hand, compliant mechanisms take advantage of recoverable deformation to transfer or transform motion, force, or energy and the benefits of compliant mechanisms mainly come from the elimination of traditional rigid joints, but the traditional displacement method reduce the stiffness of spatial compliant parallel manipulators. In this paper, a new approach of structure synthesis of 3-DoF rotational compliant parallel manipulators is proposed. Based on screw theory, the structures of RRS type 3-DoF rotational spatial compliant parallel manipulator are developed. Experiments via ANSYS are conducted to give some validation of the theoretical analysis.

Analysis of Parasitic Motion in Compliant Mechanisms Using Eigenwrenches and Eigentwists

2018 ◽  
Author(s):  
Werner W. P. J. van de Sande ◽  
Just L. Herder
Keyword(s):  
Compliant Mechanisms ◽  
Screw Theory ◽  
Compliant Mechanism ◽  
Degree Of Freedom ◽  
Compliance Matrix ◽  
Parasitic Motion ◽  
Actual Degree ◽  
Motion Metrics ◽  
Mechanism Kinematic ◽  
Kinematic Information

Parasitic motion is undesired in precision mechanisms, it causes unwanted kinematics. These erroneous motions are especially apparent in compliant mechanisms. Usually an analysis of parasitic motion is only valid for one type of mechanism. Kinematic information is imbedded in the compliance matrix of any mechanism; an eigenscrew decomposition expresses this kinematic information as screws. It uses screw theory to identify the lines along which a force yields a parallel translation and a rotation yields a parallel moment. These lines are called eigenwrenches and eigentwists. Any other load on the compliant mechanism will lead to parasitic motion. This article introduces two parasitic motion metrics using eigenscrew decomposition: the parasitic resultant from an applied screw and the deviation of an actual degree of freedom from a desired degree of freedom. These metrics are applicable to all compliant mechanism and allow comparison between two compliant mechanisms. These metrics are applied to some common compliant mechanisms as an example.

Dynamic Modeling of a Parallel Manipulator With Three Translational Degrees of Freedom

1998 ◽  
Author(s):  
Richard Stamper ◽  
Lung-Wen Tsai
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Close Agreement ◽  
Jacobian Matrix ◽  
Parallel Manipulators ◽  
Kinematic Structure ◽  
End Effector ◽  
Moving Platform ◽  
Euler Approach ◽  
Computationally Intensive

Abstract The dynamics of a parallel manipulator with three translational degrees of freedom are considered. Two models are developed to characterize the dynamics of the manipulator. The first is a traditional Lagrangian based model, and is presented to provide a basis of comparison for the second approach. The second model is based on a simplified Newton-Euler formulation. This method takes advantage of the kinematic structure of this type of parallel manipulator that allows the actuators to be mounted directly on the base. Accordingly, the dynamics of the manipulator is dominated by the mass of the moving platform, end-effector, and payload rather than the mass of the actuators. This paper suggests a new method to approach the dynamics of parallel manipulators that takes advantage of this characteristic. Using this method the forces that define the motion of moving platform are mapped to the actuators using the Jacobian matrix, allowing a simplified Newton-Euler approach to be applied. This second method offers the advantage of characterizing the dynamics of the manipulator nearly as well as the Lagrangian approach while being less computationally intensive. A numerical example is presented to illustrate the close agreement between the two models.

A novel five-degrees-of-freedom decoupled robot

Robotica ◽  
2009 ◽  
Vol 28 (6) ◽  
pp. 909-917 ◽  
Author(s):  
Jaime Gallardo-Alvarado ◽  
Horacio Orozco-Mendoza ◽  
José M. Rico-Martínez
Keyword(s):  
Machine Tools ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Solar Panels ◽  
Spatial Mechanism ◽  
Moving Platforms ◽  
Parallel Kinematic ◽  
Radar Antennas

SUMMARYIn this work a new nonoverconstrained redundant decoupled robot, free of compound joints, formed from three parallel manipulators, with two moving platforms and provided with six active limbs connected to the fixed platform, called LinceJJP, is presented. Interesting applications such as multi-axis machine tools with parallel kinematic architectures, solar panels, radar antennas, and telescopes are available for this novel spatial mechanism.

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