A Comprehensive Inverse Dynamics Problem of a Stewart Platform by Means of Lagrangian Formulation

2017 ◽  
Author(s):  
Naser Mostashiri ◽  
Alireza Akbarzadeh ◽  
Jaspreet Dhupia ◽  
Alexander Verl ◽  
Weiliang Xu
Keyword(s):  
Inverse Dynamics ◽  
Virtual Work ◽  
Stewart Platform ◽  
Joint Torques ◽  
Body Dynamics ◽  
Inverse Kinematics Problem ◽  
Simplifying Assumptions ◽  
Inverse Dynamics Problem ◽  
Multi Body ◽  
Lagrange’S Method

In this paper, using the Lagrange’s method a comprehensive inverse dynamics problem of a 6-3 UPS Stewart platform is investigated. First, the inverse kinematics problem is solved and the Jacobian matrix is derived. Next, the full inverse dynamics problem of the robot, taking into account the mass of links and inertia, is investigated and its governing equations are derived. The correctness of the dynamics equations are verified in two ways, first, using the results of the virtual work method and second using the results of a commercial multi-body dynamics software. Because the dynamic calculation is time consuming, two simplifying assumptions are considered. First, the link is assumed to have a zero mass and next it is assumed as a point mass. Studying the former assumption is rather straightforward. However, more complex equations are needed and derived in the present paper for the latter assumption. Required actuator forces for the two assumptions are compared with the case where the mass and link inertial is fully considered. It is shown that the first simplifying assumption significantly affects the accuracy of the required joint torques.

scholarly journals Inverse and forward dynamics: models of multi–body systems

2003 ◽  
Vol 358 (1437) ◽  
pp. 1493-1500 ◽  
Author(s):  
E. Otten
Keyword(s):  
Inverse Dynamics ◽  
Temporal Patterns ◽  
Forward Dynamics ◽  
Muscle Forces ◽  
Complex Behaviour ◽  
Joint Torques ◽  
Advantages And Disadvantages ◽  
Reaction Forces ◽  
Internal Forces ◽  
Multi Body

Connected multi–body systems exhibit notoriously complex behaviour when driven by external and internal forces and torques. The problem of reconstructing the internal forces and/or torques from the movements and known external forces is called the ‘inverse dynamics problem’, whereas calculating motion from known internal forces and/or torques and resulting reaction forces is called the ‘forward dynamics problem’. When stepping forward to cross the street, people use muscle forces that generate angular accelerations of their body segments and, by virtue of reaction forces from the street, a forward acceleration of the centre of mass of their body. Inverse dynamics calculations applied to a set of motion data from such an event can teach us how temporal patterns of joint torques were responsible for the observed motion. In forward dynamics calculations we may attempt to create motion from such temporal patterns, which is extremely difficult, because of the complex mechanical linkage along the chains forming the multi–body system. To understand, predict and sometimes control multi–body systems, we may want to have mathematical expressions for them. The Newton–Euler, Lagrangian and Featherstone approaches have their advantages and disadvantages. The simulation of collisions and the inclusion of muscle forces or other internal forces are discussed. Also, the possibility to perform a mixed inverse and forward dynamics calculation are dealt with. The use and limitations of these approaches form the conclusion.

Research on the Inverse Dynamics of the Flexible Multi-Body Systems for the Hybrid Polishing Kinematics Machine Tool

2006 ◽  
Vol 532-533 ◽  
pp. 53-56 ◽  
Author(s):  
Miao Yu ◽  
Ji Zhao
Keyword(s):  
Machine Tool ◽  
Parallel Mechanism ◽  
Inverse Dynamics ◽  
Dynamic Control ◽  
Free Form ◽  
Constraint Force ◽  
Body Dynamics ◽  
Multi Body ◽  
Free Form Surfaces ◽  
Polishing Tool

The hybrid polishing kinematics machine tool (HPKMT) which is made up of “3 axes parallel + 2 axes series” is developed with the specially designed elastic polishing tool system for the polishing operation on the free-form surfaces by using the characteristic of the elastic polishing adequately by the authors. In order to control the HPKMT effectively, its characteristic of the kinematics and dynamics need be known deeply. Moreover, the problem of inverse dynamics is the theory foundation to apply dynamic control of the HPKMT. The analysis of the inverse of mechanism is the important part in the research of dynamics. On the basis of the differential equations of flexible multi-body dynamics, this paper discusses on the condition of knowing the trace, posture and velocity for the end of bodies how to solve the constraint force and constraint moment of each joint on the 3- PTT parallel mechanism and two-joint series mechanism.

scholarly journals Influence of trajectories on the joint torques of kinematically redundant manipulators

2007 ◽  
Vol 29 (2) ◽  
pp. 65-72
Author(s):  
Nguyen Van Khang ◽  
Do Anh Tuan ◽  
Nguyen Phong Dien ◽  
Tran Hoang Nam
Keyword(s):  
Numerical Simulation ◽  
Inverse Dynamics ◽  
Computational Cost ◽  
Redundant Manipulators ◽  
Joint Torques ◽  
Inverse Dynamics Problem

This paper presents an algorithm for solving the inverse dynamics problem of redundant manipulators using MAPLE software. The method has the advantage of generating efficient symbolic solutions which reduces the computational cost. The influence of trajectories on the joint torques of redundant manipulators is considered. The theory is illustrated by the numerical simulation of a redundant four-link planar manipulator.

Kinematics and inverse dynamics analysis for a novel 3-PUU parallel mechanism

Robotica ◽  
2016 ◽  
Vol 35 (10) ◽  
pp. 2018-2035 ◽  
Author(s):  
Wang Liping ◽  
Xu Huayang ◽  
Guan Liwen
Keyword(s):  
Parallel Mechanism ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Virtual Work ◽  
Dynamics Analysis ◽  
Parasitic Motion ◽  
Inverse Kinematics Problem ◽  
Geometrical Constraints ◽  
Inverse Dynamics Analysis ◽  
Matrix Calculation

SUMMARYThe modules of parallel tool heads with 2R1T degrees of freedom (DOFs), i.e., two rotational DOFs and one translational DOF, have become so important in the field of machine tools that corresponding research studies have attracted extensive attention from both academia and industry. A 3-PUU (P represents a prismatic joint, U represents a universal joint) parallel mechanism with 2R1T DOFs is proposed in this paper, and a detailed discussion about its architecture, geometrical constraints, and mobility characteristics is presented. Furthermore, on the basis of its special geometrical constraint, we derive and explicitly express the parasitic motion of the 3-PUU mechanism. Then, the inverse kinematics problem, the Jacobian matrix calculation and the forward kinematics problem are also investigated. Finally, with a simplified dynamics model, the inverse dynamics analysis for the mechanism is carried out with the Principle of Virtual Work, and corresponding results are compared with that of the 3-PRS mechanism. The above analyses illustrate that the 3-PUU parallel mechanism has good dynamics features, which validates the feasibility of applying this mechanism as a tool head module.

A Numerical and Experimental Analysis of a Chain of Flexible Bodies

1994 ◽  
Vol 116 (1) ◽  
pp. 73-80 ◽  
Author(s):  
Marco Giovagnoni
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Numerical Data ◽  
Small Displacement ◽  
Flexible Bodies ◽  
Rigid Link ◽  
Body Dynamics ◽  
A Chain ◽  
Multi Body ◽  
Kinematic Solution

A flexible multi-body dynamics approach is described. It uses an equivalent rigid link system from which are measured small displacements. The equations of motion are obtained by direct application of the principle of virtual work. Some terms in the virtual and real components have been neglected by virtue of the small displacement assumption. The use of sensitivity coefficients allows one to obtain a formulation which can be easily interfaced with any kinematic solution algorithm. It also enables one to check the correctness of the chosen equivalent rigid link system. The theory is then employed to reproduce numerically the experimental recordings obtained from a flexible linkage. Agreement between experimental and numerical data is good.

scholarly journals Normal form approach in the motion planning of space robots: a case study

2021 ◽  
Author(s):  
Krzysztof Tchoń ◽  
Katarzyna Zadarnowska
Keyword(s):  
Normal Form ◽  
Motion Planning ◽  
Normal Forms ◽  
Inverse Dynamics ◽  
Planning Problem ◽  
Inverse Dynamics Problem ◽  
Velocity Level ◽  
Form Approach ◽  
Space Approach

AbstractWe examine applicability of normal forms of non-holonomic robotic systems to the problem of motion planning. A case study is analyzed of a planar, free-floating space robot consisting of a mobile base equipped with an on-board manipulator. It is assumed that during the robot’s motion its conserved angular momentum is zero. The motion planning problem is first solved at velocity level, and then torques at the joints are found as a solution of an inverse dynamics problem. A novelty of this paper lies in using the chained normal form of the robot’s dynamics and corresponding feedback transformations for motion planning at the velocity level. Two basic cases are studied, depending on the position of mounting point of the on-board manipulator. Comprehensive computational results are presented, and compared with the results provided by the Endogenous Configuration Space Approach. Advantages and limitations of applying normal forms for robot motion planning are discussed.

scholarly journals Estimating maximum bite performance in Tyrannosaurus rex using multi-body dynamics

2012 ◽  
Vol 8 (4) ◽  
pp. 660-664 ◽  
Author(s):  
K. T. Bates ◽  
P. L. Falkingham
Keyword(s):  
Body Size ◽  
Feeding Behaviour ◽  
Ontogenetic Change ◽  
Positive Allometry ◽  
Musculoskeletal Models ◽  
Terrestrial Animal ◽  
Body Dynamics ◽  
Mode Of Life ◽  
Scaling Analyses ◽  
Multi Body

Bite mechanics and feeding behaviour in Tyrannosaurus rex are controversial. Some contend that a modest bite mechanically limited T. rex to scavenging, while others argue that high bite forces facilitated a predatory mode of life. We use dynamic musculoskeletal models to simulate maximal biting in T. rex . Models predict that adult T. rex generated sustained bite forces of 35 000–57 000 N at a single posterior tooth, by far the highest bite forces estimated for any terrestrial animal. Scaling analyses suggest that adult T. rex had a strong bite for its body size, and that bite performance increased allometrically during ontogeny. Positive allometry in bite performance during growth may have facilitated an ontogenetic change in feeding behaviour in T. rex , associated with an expansion of prey range in adults to include the largest contemporaneous animals.

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