Kinematics and Singularity Analysis of a 2R2T Parallel Mechanism

2015 ◽  
Author(s):  
Wei Ye ◽  
Yuefa Fang ◽  
Sheng Guo
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Design Stage ◽  
Forward Kinematics ◽  
Medical Applications ◽  
Moving Platforms ◽  
Forward And Inverse Kinematics ◽  
Displacement Group

In this paper, we focus our attention on a parallel mechanism with four identical limbs and two moving platforms that are connected by a prismatic joint. Firstly, the degrees of freedom analysis of the mechanism is conducted based on the displacement group theory. Both the two moving platforms have the ability to perform two rotational and two translational motions (2R2T). Secondly, forward and inverse kinematics of the proposed mechanism is analyzed, closed-from solutions are obtained for the forward kinematics. Finally, three types of singularity, i.e. limb singularity, actuation singularity and platform singularity of the 2R2T parallel mechanism are analyzed. No limb singularity and platform singularity is found and the actuation singularity can be avoided in the design stage. The proposed mechanism has the potential to be used in industry and medical applications.

Kinematics of a planar slider-crank linkage in screw form

2021 ◽  
pp. 095440622110207
Author(s):  
Jing-Shan Zhao ◽  
Songtao Wei ◽  
Junjie Ji
Keyword(s):  
Angular Velocity ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Numerical Algorithms ◽  
Forward Kinematics ◽  
End Effector ◽  
First Order ◽  
Forward And Inverse Kinematics ◽  
Definition Of ◽  
Inverse Velocity

This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

Kinematic Analysis of a Three-DOF Parallel Mechanism for Telescope Applications

1997 ◽  
Author(s):  
J. A. Carretero ◽  
M. Nahon ◽  
B. Buckham ◽  
C. M. Gosselin
Keyword(s):  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Jacobian Matrix ◽  
Constraint Equations ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degree Of Freedom ◽  
Three Degrees Of Freedom

Abstract This paper presents a kinematic analysis of a three-degree-of-freedom parallel mechanism intended for use as a telescope mirror focussing device. The construction of the mechanism is first described and its forward and inverse kinematics solutions are derived. Because the mechanism has only three degrees of freedom, constraint equations must be generated to describe the inter-relationship between the six Cartesian coordinates which describe the position and orientation of the moving platform. Once these constraints are incorporated into the kinematics model, a constrained Jacobian matrix is obtained. The stiffness and dexterity properties of the mechanism are then determined based on this Jacobian matrix. The mechanism is shown to exhibit desirable properties in the region of its workspace of interest in the telescope focussing application.

A Hybrid Self-Stressed Cable-Driven Mechanism

2008 ◽  
Author(s):  
Saeed Behzadipour
Keyword(s):  
Static Loading ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Tensile Force ◽  
Cable System ◽  
End Effector ◽  
Stiffness Analysis ◽  
Cable Length ◽  
Cable Drive ◽  
Forward And Inverse Kinematics

A new hybrid cable-driven manipulator is introduced. The manipulator is composed of a Cartesian mechanism to provide three translational degrees of freedom and a cable system to drive the mechanism. The end-effector is driven by three rotational motors through the cables. The cable drive system in this mechanism is self-stressed meaning that the pre-tension of the cables which keep them taut is provided internally. In other words, no redundant actuator or external force is required to maintain the tensile force in the cables. This simplifies the operation of the mechanism by reducing the number of actuators and also avoids their continuous static loading. It also eliminates the redundant work of the actuators which is usually present in cable-driven mechanisms. Forward and inverse kinematics problems are solved and shown to have explicit solutions. Static and stiffness analysis are also performed. The effects of the cable’s compliance on the stiffness of the mechanism is modeled and presented by a characteristic cable length. The characteristic cable length is calculated and analyzed in representative locations of the workspace.

A Model of the Human Spine: Forward and Inverse Kinematics

1992 ◽  
Author(s):  
Sunil Kumar Agrawal ◽  
Siyan Li ◽  
Glen Desmier
Keyword(s):  
Range Of Motion ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Joint Angles ◽  
Human Spine ◽  
Forward And Inverse Kinematics ◽  
Position And Orientation ◽  
Three Degrees Of Freedom ◽  
Adjacent Vertebra

Abstract The human spine is a sophisticated mechanism consisting of 24 vertebrae which are arranged in a series-chain between the pelvis and the skull. By careful articulation of these vertebrae, a human being achieves fine motion of the skull. The spine can be modeled as a series-chain with 24 rigid links, the vertebrae, where each vertebra has three degrees-of-freedom relative to an adjacent vertebra. From the studies in the literature, the vertebral geometry and the range of motion between adjacent vertebrae are well-known. The objectives of this paper are to present a kinematic model of the spine using the available data in the literature and an algorithm to compute the inter vertebral joint angles given the position and orientation of the skull. This algorithm is based on the observation that the backbone can be described analytically by a space curve which is used to find the joint solutions..

scholarly journals Optimum Seeking of Redundant Actuators for M-RCM 3-UPU Parallel Mechanism

2020 ◽  
Author(s):  
Chen Zhao ◽  
Jingke Song ◽  
Xuechan Chen ◽  
Ziming Chen ◽  
Huafeng Ding
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Universal Joint ◽  
Prismatic Joint ◽  
Transmission Index ◽  
Redundant Actuators ◽  
Force Transmissibility ◽  
Singular Configuration

Abstract This paper focuses on a 2R1T 3-UPU (U for universal joint and P for prismatic joint) parallel mechanism (PM) with two rotational and one translational (2R1T) degrees of freedom (DOFs) and the ability of multiple remote centers of motion (M-RCM). The singularity analysis based on the indexes of motion/force transmissibility and constraint shows that this PM has transmission singularity, constraint singularity, mixed singularity and limb singularity. To solve these singularproblems, the quantifiable redundancy transmission index (RTI) and the redundancy constraint index (RCI) are proposed for optimum seeking of redundant actuators for this PM. Then the appropriate redundant actuators are selected and the working scheme for redundant actuators near the corresponding singular configuration are given to help the PM go through the singularity.

scholarly journals Stability and Gait Planning of 3-UPU Hexapod Walking Robot

Robotics ◽  
2018 ◽  
Vol 7 (3) ◽  
pp. 48 ◽  
Author(s):  
Ruiqin Li ◽  
Hongwei Meng ◽  
Shaoping Bai ◽  
Yinyin Yao ◽  
Jianwei Zhang
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Step Length ◽  
Parallel Robot ◽  
Search Method ◽  
Walking Robot ◽  
Gait Control ◽  
Gait Planning ◽  
Forward And Inverse Kinematics ◽  
Passing Ability

The paper presents an innovative hexapod walking robot built with 3-UPU parallel mechanism. In the robot, the parallel mechanism is used as both an actuator to generate walking and also a connecting body to connect two groups of three legs, thus enabling the robot to walk with simple gait by very few motors. In this paper, forward and inverse kinematics solutions are obtained. The workspace of the parallel mechanism is analyzed using limit boundary search method. The walking stability of the robot is analyzed, which yields the robot’s maximum step length. The gait planning of the hexapod walking robot is studied for walking on both flat and uneven terrains. The new robot, combining the advantages of parallel robot and walking robot, has a large carrying capacity, strong passing ability, flexible turning ability, and simple gait control for its deployment for uneven terrains.

scholarly journals Analytical inverse kinematics for 5-DOF humanoid manipulator under arbitrarily specified unconstrained orientation of end-effector

Robotica ◽  
2014 ◽  
Vol 33 (4) ◽  
pp. 747-767 ◽  
Author(s):  
Masayuki Shimizu
Keyword(s):  
Analytical Method ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Singularity Analysis ◽  
Inverse Kinematic ◽  
Inverse Kinematic Problem ◽  
Target Orientation ◽  
End Effector ◽  
Position And Orientation

SUMMARYThis paper proposes an analytical method of solving the inverse kinematic problem for a humanoid manipulator with five degrees-of-freedom (DOF) under the condition that the target orientation of the manipulator's end-effector is not constrained around an axis fixed with respect to the environment. Since the number of the joints is less than six, the inverse kinematic problem cannot be solved for arbitrarily specified position and orientation of the end-effector. To cope with the problem, a generalized unconstrained orientation is introduced in this paper. In addition, this paper conducts the singularity analysis to identify all singular conditions.

A Novel Parallel Mechanism With 3-RRUR Legs

2007 ◽  
Author(s):  
Yanwen Li ◽  
Yueyue Zhang ◽  
Lumin Wang ◽  
Zhen Huang
Keyword(s):  
Machine Tools ◽  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Parallel Manipulators ◽  
Forward Kinematics ◽  
Symmetrical Structure ◽  
Forward Kinematic ◽  
Accumulated Error

This paper investigates a novel 4-DOF 3-RRUR parallel manipulator, the number and the characteristics of its degrees of freedom are determined firstly, the rational input plan and the invert and forward kinematic solutions are carried out then. The corresponding numeral example of the forward kinematics is given. This type of parallel manipulators has a symmetrical structure, less accumulated error, and can be used to construct virtual-axis machine tools. The analysis in this paper will play an important role in promoting the application of such manipulators.

Analysis of a mechanism with redundant drive for antenna pointing

2016 ◽  
Vol 231 (2) ◽  
pp. 229-239 ◽  
Author(s):  
Xin Li ◽  
Xilun Ding ◽  
Gregory S Chirikjian
Keyword(s):  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Numerical Examples ◽  
Pointing Device ◽  
Key Factor ◽  
Rotary Motors ◽  
Redundantly Actuated ◽  
Pointing Accuracy ◽  
Forward And Inverse Kinematics ◽  
Redundant Drive

Orientation accuracy is a key factor in the design of mechanisms for antenna pointing. Our design uses a redundantly actuated parallel mechanism which may provide an effective way to solve this problem, and even can increase its payload capability and reliability. The presented mechanism can be driven by rotary motors fixed on the base to reduce the inertia of the moving parts and to lower the power consumption. The mechanism is redundantly actuated by three arms, and is used as a two-dimensional antenna tracking and pointing device. Both the forward and inverse kinematics are investigated to find all the possible solutions. Detailed characters of the platform are analyzed to demonstrate the advantages in eliminating singularities and improving pointing accuracy. A method of calculating the overconstrained orientational error is also proposed based on the differential kinematics. All the methods are verified by numerical examples.

Analysis of the Kinematics of an Eight-Wheeled Mobile Platform

2013 ◽  
Vol 198 ◽  
pp. 67-72
Author(s):  
Marek Stania
Keyword(s):  
Inverse Kinematics ◽  
Object Motion ◽  
Forward Kinematics ◽  
Contact Phenomenon ◽  
Kinematics Model ◽  
Inverse Kinematics Problem ◽  
Transport Vehicle ◽  
Forward And Inverse Kinematics ◽  
Motion Parameters ◽  
Simulation Results

This paper presents the modeling problem connected with the autonomous transport vehicle designed at Hochschule Ravensburg-Weingarten. The forward and inverse kinematics problem of eight-wheeled autonomous transport vehicle have been formulated and solved, additionally examples of simulation results representing the changes of individual motion parameters have been presented. Contact phenomenon between foundation and drive wheel has been taken into account in the kinematics model. Motion trajectory and velocity of the selected point belonging to the platform have been intended while the inverse kinematics problem has been solved. The forward kinematics problem has been worked out in order to verify correctness of the studied kinematics model. The presented simulation results point out compatibility of the worked out kinematics model of investigated object. The worked out models allow carrying out analysis of object motion through simulation investigations on the basis of proposed computational model.

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