scholarly journals The Inverse Dynamics of a 3-DOF Parallel Mechanism Based on Analytical Forward Kinematics

2020 ◽  
Author(s):  
Ke Wang ◽  
Ju Li ◽  
Huiping Shen ◽  
Jingjing You ◽  
Ting-Li Yang
Keyword(s):  
Dynamic Equation ◽  
Driving Force ◽  
Theoretical Basis ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Forward Kinematics ◽  
Forward Solution ◽  
Inverse Dynamic ◽  
New Type

Abstract A new type of 3-dof parallel mechanism(PM) with analytical position forward solution is proposed. The reverse dynamic equation of the PM is solved. Different from the traditional dynamic analysis using inverse kinematics, the displacement, velocity and acceleration equations of the PM are established and solved by forward kinematics.The inverse dynamic equation of the PM is constructed and solved by analyzing the forces on each link and based on Newton-Euler method.Through MATLAB and ADAMS , the inverse dynamics is verified by an example. The maximum driving force error of each actuated pair is 1.32%, 5.8% and 5.2% respectively.This paper provides a theoretical basis for the design, manufacture and application of the PM.

Inverse Dynamics of 2UPS-RPU Parallel Mechanism by Newton-Euler Formation

2010 ◽  
Vol 29-32 ◽  
pp. 738-743
Author(s):  
Wen Hua Wang ◽  
Zhi You Feng ◽  
Ting Li Yang
Keyword(s):  
Computer Simulation ◽  
Dynamic Equation ◽  
Driving Force ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Inverse Dynamic ◽  
Moving Platform

2UPS-RPU is a new 4-DOF parallel mechanism with serial input limb. In this paper, the inverse dynamic equation of this mechanism is formulated by Newton-Euler formation based on each limb and moving platform as the studying objects. The inverse kinematics of the mechanism is analyzed. The driving force, driving moment and the constraint moment can be obtained. Finally, a computer simulation is carried out to solve the inverse dynamics of the mechanism when the motion of moving platform is given.

Inverse Dynamic Analysis and Linearisation of a High Speed Parallel Mechanism

2005 ◽  
Author(s):  
M. Necip Sahinkaya ◽  
Yanzhi Li
Keyword(s):  
Dynamic Analysis ◽  
Parallel Mechanism ◽  
High Speed ◽  
Inverse Dynamics ◽  
Motion Path ◽  
Model Parameters ◽  
Control Input ◽  
Inverse Dynamic ◽  
Inverse Dynamic Analysis ◽  
Dynamics Models

Inverse dynamic analysis of a three degree of freedom parallel mechanism driven by three electrical motors is carried out to study the effect of motion speed on the system dynamics and control input requirements. Availability of inverse dynamics models offer many advantages, but controllers based on real-time inverse dynamic simulations are not practical for many applications due to computational limitations. An off-line linearisation of system and error dynamics based on the inverse dynamic analysis is developed. It is shown that accurate linear models can be obtained even at high motion speeds eliminating the need to use computationally intensive inverse dynamics models. A point-to-point motion path for the mechanism platform is formulated by using a third order exponential function. It is shown that the linearised model parameters vary significantly at high motion speeds, hence it is necessary to use adaptive controllers for high performance.

Inverse Dynamics of 2UPS-2RPS Parallel Mechanism Based on Virtual Work Principle

2010 ◽  
Vol 29-32 ◽  
pp. 744-749 ◽  
Author(s):  
Wen Hua Wang ◽  
Zhi You Feng ◽  
Ting Li Yang ◽  
Ce Zhang
Keyword(s):  
Computer Simulation ◽  
Kinematic Analysis ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Dynamic Equations ◽  
Inverse Dynamic ◽  
Virtual Work Principle ◽  
Inverse Dynamic Model ◽  
Moving Platform

Inverse dynamic equations of the 2UPS-2RPS mechanism are formulated by utilizing the virtual work principle. Kinematic analysis of the mechanism is presented, on the basis of which the Jacobian matrices of the limbs and the mechanism are deduced. By combining the dynamics of the limbs and the moving-platform, the inverse dynamic model of the mechanism is obtained. Finally a computer simulation is carried out to demonstrate the dynamic analysis of the moving platform.

scholarly journals Forward and Inverse Dynamics of a Six-Axis Accelerometer Based on a Parallel Mechanism

Sensors ◽  
2021 ◽  
Vol 21 (1) ◽  
pp. 233
Author(s):  
Linkang Wang ◽  
Jingjing You ◽  
Xiaolong Yang ◽  
Huaxin Chen ◽  
Chenggang Li ◽  
...  
Keyword(s):  
Configuration Space ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Recursive Algorithm ◽  
Hamiltonian Function ◽  
Euler Method ◽  
Dynamic Equations ◽  
Sensor Calibration ◽  
Inverse Dynamic ◽  
New Strategy

The solution of the dynamic equations of the six-axis accelerometer is a prerequisite for sensor calibration, structural optimization, and practical application. However, the forward dynamic equations (FDEs) and inverse dynamic equations (IDEs) of this type of system have not been completely solved due to the strongly nonlinear coupling relationship between the inputs and outputs. This article presents a comprehensive study of the FDEs and IDEs of the six-axis accelerometer based on a parallel mechanism. Firstly, two sets of dynamic equations of the sensor are constructed based on the Newton–Euler method in the configuration space. Secondly, based on the analytical solution of the sensor branch chain length, the coordination equation between the output signals of the branch chain is constructed. The FDEs of the sensor are established by combining the coordination equations and two sets of dynamic equations. Furthermore, by introducing generalized momentum and Hamiltonian function and using Legendre transformation, the vibration differential equations (VDEs) of the sensor are derived. The VDEs and Newton–Euler equations constitute the IDEs of the system. Finally, the explicit recursive algorithm for solving the quaternion in the equation is given in the phase space. Then the IDEs are solved by substituting the quaternion into the dynamic equations in the configuration space. The predicted numerical results of the established FDEs and IDEs are verified by comparing with virtual and actual experimental data. The actual experiment shows that the relative errors of the FDEs and the IDEs constructed in this article are 2.21% and 7.65%, respectively. This research provides a new strategy for further improving the practicability of the six-axis accelerometer.

The Dynamic Analysis of a 2-PRR Planar Parallel Mechanism

2005 ◽  
Vol 219 (9) ◽  
pp. 901-909 ◽  
Author(s):  
L-P Wang ◽  
J-S Wang ◽  
J Chen
Keyword(s):  
Parallel Mechanism ◽  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Driving Forces ◽  
Inverse Dynamic ◽  
Inverse Dynamic Model ◽  
Planar Parallel Manipulator ◽  
Euler Approach ◽  
Motion Parameters

The article presents the inverse dynamics of a two-degrees-of-freedom planar parallel manipulator by the Newton-Euler approach. On the basis of the inverse dynamic model, the driving forces of actuators are simulated in different motion parameters. Further, the effects of inertia of each moving component to the driving forces are computed through the numerical method.

Forward Kinematics of Six-DOF Parallel Robot Based on Adaptive Differential Evolution

2013 ◽  
Vol 303-306 ◽  
pp. 1674-1677 ◽  
Author(s):  
Liang Shun Ma ◽  
Kuang Rong Hao ◽  
Yong Sheng Ding
Keyword(s):  
Differential Evolution ◽  
Inverse Kinematics ◽  
Differential Evolution Algorithm ◽  
Parallel Robot ◽  
Forward Kinematics ◽  
Forward Solution ◽  
Adaptive Parameters ◽  
Adaptive Differential Evolution ◽  
Six Dof ◽  
Evolution Algorithm

Parallel robot inverse kinematics solution is relatively easier to obtain than forward kinematics forward, this paper assumes that the forward kinematics of six-DOF parallel robot is given then using the kinematics inverse solution to approximate the forward solution. To improve efficiency and stability of the approximation, an adaptive parameters differential evolution algorithm is proposed and applied to the forward kinematics problem. The experimental results show that the modified algorithm can gain the forward kinematics of parallel robot efficiently.

Kinetostatic Analysis and Design Optimization of the Tricept Machine Tool Family

2002 ◽  
Vol 124 (3) ◽  
pp. 725-733 ◽  
Author(s):  
Dan Zhang ◽  
Cle´ment M. Gosselin
Keyword(s):  
Machine Tool ◽  
Inverse Kinematics ◽  
Parallel Mechanism ◽  
Mechanical Design ◽  
Geometric Model ◽  
Flexible Link ◽  
Analysis And Design ◽  
New Type ◽  
Link Flexibility ◽  
Kinetostatic Model

Selecting a mechanism for a machine tool that will best suit the needs of a forecast set of rigidities can be a difficult and costly exercise. This problem can now be addressed using a kinetostatic modeling method. In this paper, a kinetostatic model for the Tricept machine tool family is established based on lumped flexibilities. This model can be used to analyze the effect of link flexibility on the machine tool’s global stiffness and the platform positioning precision. The Tricept machine tool is a new type of parallel mechanism with prismatic actuators whose degree of freedom is dependent on a passive constraining leg connecting the base and the platform. The geometric model and the mechanical design of the Tricept machine tool is first recalled. Then, a lumped kinetostatic model is proposed in order to account for joint and link compliances. It is shown that the link flexibility has a significant effect on the machine tool’s precision and that it is necessary to take the link flexibility into account. Additionally, the inverse kinematics and velocity equations are given for both rigid-link and flexible-link mechanisms. Finally, the optimization of the stiffness is addressed using a genetic algorithm.

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.

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.

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