Udwadia-Kalaba Approach for Parallel Manipulator Dynamics

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Jin Huang ◽  
Y. H. Chen ◽  
Zhihua Zhong
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Equation Of Motion ◽  
Dynamics Analysis ◽  
Constraint Forces ◽  
Kinematic Constraints ◽  
Manipulator Dynamics ◽  
Stewart Gough Platform

A novel Udwadia-Kalaba approach for parallel manipulator dynamics analysis is presented. The approach segments a parallel manipulator system into several leg-subsystems and the platform subsystem, which are connected by kinematic constraints. The Udwadia-Kalaba equation is then used to calculate the constraint forces due to the constraints. Based on this, the equation of motion, which is an explicit (i.e., closed) form, can be formulated. The method allows a systematic procedure to generate the dynamic model for both direct dynamics and inverse dynamics without invoking additional variables (such as multipliers or quasi-variables), nor does it require projection. A classical parallel Stewart-Gough platform is chosen to demonstrate the feasibility and advantages of this approach.

An efficient method for the dynamic modeling and analysis of Stewart parallel manipulator based on the screw theory

2019 ◽  
Vol 234 (3) ◽  
pp. 808-821
Author(s):  
Yulei Hou ◽  
Guoxing Zhang ◽  
Daxing Zeng
Keyword(s):  
Dynamic Model ◽  
Dynamic Modeling ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Screw Theory ◽  
Parallel Manipulators ◽  
Force Balance ◽  
Constraint Matrix ◽  
Scheme Design ◽  
Control Scheme

Dynamic modeling serves as the fundamental basis for dynamic performance analysis and is an essential aspect of the control scheme design of parallel manipulators. This report presents a concise and efficient solution to the dynamics of Stewart parallel manipulators based on the screw theory. The initial pose of these manipulators is described. Then the pose matrix of each link of the Stewart parallel mechanism is obtained using an inverse kinematics solution and an exponential product formula. Considering the constraint relationship between joints, the constraint matrix of the Stewart parallel manipulator is deduced. In addition, the Jacobian matrix and the twist of each link are obtained. Moreover, by deriving the differential form of the constraint matrix, the spatial acceleration of each link is obtained. Based on the force balance relationship of each link, the inverse dynamics and the general form of the dynamic model of the Stewart parallel manipulator is established and the process of inverse dynamics is summarized. The dynamic model is then verified via dynamic simulation using the ADAMS software. A numerical example is considered to demonstrate the feasibility and effectiveness of this model. The proposed dynamic modeling approach serves as a fundamental basis for structural optimization and control scheme design of the Stewart parallel manipulators.

Gait Analysis Using Multibody Simulation Tools and Inverse Dynamics Procedures

2005 ◽  
Author(s):  
Miguel Silva ◽  
Jorge Ambro´sio
Keyword(s):  
Gait Analysis ◽  
Inverse Dynamics ◽  
Three Dimensional ◽  
Biomechanical Model ◽  
Whole Body ◽  
Dynamics Analysis ◽  
Natural Coordinates ◽  
Kinematic Constraints ◽  
Biomechanical Models ◽  
Inverse Dynamics Analysis

The use of inverse dynamics methodologies for the evaluation of intersegmental reaction forces and the moments-of-force at the anatomical joints, in the framework of gait analysis, not only requires that appropriate biomechanical models are used but also that kinematic and kinetic data sets are available. This paper discusses the quality of the results of the inverse dynamics analysis with respect to the filtering procedures used and the kinematic consistency of the position, velocity and acceleration data. A three-dimensional whole body response biomechanical model based on a multibody formulation with natural coordinates is used. The model has 16 anatomical segments that are described using 33 rigid bodies in a total of 44 degrees-of-freedom. In biomechanical applications, one of the advantages of the current formulation is that the set of anatomical points used to reconstruct the spatial motion of the subject is also used to construct the set of natural coordinates that describe the biomechanical model itself. Based on the images collected by four synchronized video cameras, the three-dimensional trajectories of the anatomical points are reconstructed using standard photogrammetry techniques and Direct Linear Transformations. The trajectories obtained are then filtered in order to reduce the noise levels introduced during the reconstruction procedure using 2nd order Butterworth low-pass filters with properly chosen cut-off frequencies. The filtered data is used in the inverse dynamics analysis either directly or after being modified in order to ensure its consistency with the biomechanical model’s kinematic constraints. It is also shown that the use of velocities and accelerations consistent with the kinematic constraints or those obtained through the time derivatives of the spline interpolation curves of the reconstructed trajectories lead to similar results.

The Closed-Form Equation of Motion of a Human Body With Joint Friction

2013 ◽  
Author(s):  
Qingmin Huang ◽  
Ye-Hwa Chen ◽  
Xin Nie
Keyword(s):  
Closed Form ◽  
Human Body ◽  
Free Fall ◽  
Analytic Form ◽  
Equation Of Motion ◽  
Friction Torque ◽  
Constraint Forces ◽  
Constraint Force ◽  
Joint Friction ◽  
And Control

A general method for equation of motion of a human body is presented. The equation is in closed-form (i.e., analytic form). A hierarchical approach is introduced to get the equation of motion of the human body. The constraint force between subsystems is explicitly obtained which can be used to calculate the joint friction torque. The final equation of motion includes the dynamics of the unconstrained motion, the constraints, and the constraint forces including the joint friction torque induced by the nonideal constraints. No auxiliary variables such as Lagrange multipliers or pseudo-generalized speeds are needed. Therefore the equation of motion is most suitable for generic dynamic analysis and control design. A four-segment, planar, articulated linkage free fall human body is chosen to demonstrate this method.

Inverse dynamics of the 6-dof out-parallel manipulator by means of the principle of virtual work

Robotica ◽  
2009 ◽  
Vol 27 (2) ◽  
pp. 259-268 ◽  
Author(s):  
Yongjie Zhao ◽  
Feng Gao
Keyword(s):  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Principle Of Virtual Work ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Robot System ◽  
Lead Screw ◽  
Moving Platform

SUMMARYIn this paper, the inverse dynamics of the 6-dof out-parallel manipulator is formulated by means of the principle of virtual work and the concept of link Jacobian matrices. The dynamical equations of motion include the rotation inertia of motor–coupler–screw and the term caused by the external force and moment exerted at the moving platform. The approach described here leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure. Numerical simulation for the inverse dynamics of a 6-dof out-parallel manipulator is illustrated. The whole actuating torques and the torques caused by gravity, velocity, acceleration, moving platform, strut, carriage, and the rotation inertia of the lead screw, motor rotor and coupler have been computed.

FUZZY LOGIC-BASED INVERSE DYNAMIC MODELLING OF ROBOT MANIPULATORS

2010 ◽  
Vol 34 (1) ◽  
pp. 137-150 ◽  
Author(s):  
Meysar Zeinali ◽  
Leila Notash
Keyword(s):  
Fuzzy Logic ◽  
Dynamic Model ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Robot Manipulators ◽  
Dynamic Modelling ◽  
Inverse Dynamic ◽  
Model Based ◽  
Uncertain Dynamics ◽  
Modelling Methodology

This paper presents the design and implementation of a systematic fuzzy modelling methodology for the inverse dynamic modelling of robot manipulators. The fuzzy logic modelling methodology is motivated in part by the difficulties encountered in the modelling of complex nonlinear uncertain systems, and by the objective of developing an efficient dynamic model for the real-time model-based control. The methodology is applied to build the fuzzy logic-based inverse dynamic model of a prototyped wire-actuated parallel manipulator with uncertain dynamics. The developed inverse dynamics has been used in a fuzzy model-based adaptive robust controller for the tracking control of the parallel manipulator.

Inverse Dynamics of Constrained Multibody Systems

1990 ◽  
Vol 57 (3) ◽  
pp. 750-757 ◽  
Author(s):  
J. T. Wang
Keyword(s):  
Multibody Systems ◽  
Inverse Dynamics ◽  
Multibody System ◽  
Coefficient Matrix ◽  
Force Term ◽  
Constraint Forces ◽  
Kinematic Constraints ◽  
Constrained Multibody Systems ◽  
Orthogonal Complement Matrix ◽  
Partial Velocity

A method for analyzing constrained multibody systems is presented. The method is applicable to a class of problems in which the multibody system is subjected to both force and kinematic constraints. This class of problems cannot be solved by using the classical methods. The method is based upon the concept of partial velocity and generalized forces of Kane’s method to permit the choice of constraint forces for fulfilling both kinematic and force constraints. Thus, the constraint forces or moments at convenient points or bodies may be specified in any desired form. For many applications, the method also allows analysts to choose a constant coefficient matrix for the undetermined force term to greatly reduce the burden of repeatedly computing its orthogonal complement matrix in solving the differential algebraic dynamic equations. Two examples illustrating the concepts are presented.

Differential kinematics of parallel manipulators using Assur virtual chains

2009 ◽  
Vol 223 (7) ◽  
pp. 1697-1711 ◽  
Author(s):  
A Campos ◽  
R Guenther ◽  
D Martins
Keyword(s):  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Screw Theory ◽  
Kinematic Chain ◽  
Parallel Manipulators ◽  
Kinematic Constraints ◽  
Passive Joint ◽  
Planar Parallel Manipulator ◽  
Stewart Gough Platform ◽  
Homogeneous Linear

This article introduces the concept of Assur virtual chains and its applications in differential kinematics of parallel manipulators. Using Assur virtual chains, the differential kinematics has a simple matricial formulation and the choice between direct and inverse kinematics is reduced to select primary variables in a homogeneous linear system. Assur virtual chains are also useful for obtaining information about the relative movements or to imposing particular kinematic constraints between two links of a kinematic chain. Additionally, a new systematic algorithm is established to analytically eliminate passive joint velocities and calculate the Jacobian matrices. This elimination approach is based on screw theory concepts such as twist, wrench, and reciprocity; also, graph theory is used for kinematic chain representation. At the end of the article, the method is applied to a 3RRR planar parallel manipulator and a general universal-prismatic-spheric Stewart—Gough platform.

Automatic Model Generation for Modular Reconfigurable Robot Dynamics

1998 ◽  
Vol 120 (3) ◽  
pp. 346-352 ◽  
Author(s):  
I-Ming Chen ◽  
Guilin Yang
Keyword(s):  
Closed Form ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Dynamic Models ◽  
Equation Of Motion ◽  
Robot Dynamics ◽  
Model Generation ◽  
Modular Robot ◽  
Form Equation ◽  
Automatic Model Generation

In control and simulation of a modular robot system, which consists of standardized and interconnected joint and link units, manual derivation of its dynamic model needs tremendous effort because these models change all the time as the robot geometry is altered after module reconfiguration. This paper presents a method to automate the generation of the closed-form equation of motion of a modular robot with arbitrary degrees-of-freedom and geometry. The robot geometry we consider here is branching type without loops. A graph technique, termed kinematic graphs and realized through assembly incidence matrices (AIM) is introduced to represent the module assembly sequence and robot geometry. The formulation of the dynamic model is started with recursive Newton-Euler algorithm. The generalized velocity, acceleration, and forces are expressed in terms of linear operations on se(3), the Lie algebra of the Euclidean group SE(3). Based on the equivalence relationship between the recursive formulation and the closed-form Lagrangian formulation, the accessibility matrix of the kinematic graph of the robot is used to assist the construction of the closed-form equation of motion of a modular robot. This automatic model generation technique can be applied to the control of rapidly reconfigurable robotic workcells and other automation equipment built around modular components that require accurate dynamic models.

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