Synthetic Wheel Prismatic Joint Biped With Torso

2009 ◽  
Author(s):  
Louis L. Flynn ◽  
Rouhollah Jafari ◽  
Ranjan Mukherjee
Keyword(s):  
Closed Loop ◽  
Equations Of Motion ◽  
Biped Robot ◽  
Torque Control ◽  
Free Motion ◽  
Walking Gait ◽  
Prismatic Joint ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

The design of a new biped robot is proposed in this paper. Based on the concept of a self-propelled wheel, the design offers to provide impact-free motion during walking. The biped robot is composed of a torso and two legs. Each leg has arc-shaped feet that are constrained to move in a manner that essentially allows the robot to roll continuously during walking. The role of the torso is to generate forward and backward motion. The equations of motion of the robot are generated using Lagrange’s equations and constraints are imposed on the motion to generate a walking gait. In the experimental hardware, the constraints are imposed by designing and implementing closed-loop torque control of the actuators. The robot successfully walked down a hallway and data collected from the robot verified the efficacy of the controllers.

On the Kinematics and Kinetics of Mechanical Seals, Rotors, and Wobbling Bodies

2005 ◽  
Author(s):  
Itzhak Green
Keyword(s):  
Equations Of Motion ◽  
Mechanical Seals ◽  
Kinematical Constraint ◽  
Lagrange’S Equations ◽  
Dynamic Analyses ◽  
Kinematical Model ◽  
Kinetics Of ◽  
Kinematics And Kinetics ◽  
Lagrange's Equations

Mechanical seals, rotors, and wobbling bodies are characterized by a kinematical constraint that prevents them from having integral motion with respect to their own frame. A valid kinematical model is a prerequisite to subsequent dynamic analyses. Three previous works have suggested distinctly different kinematical models to the same problem. The analysis herein presents yet another kinematical model that preserves (actually enforces) the proper kinematical constraint. The outcome reaffirms one of the previous models. The equations of motion are derived using Lagrange’s equations to complement results obtained previously by Newton-Euler mechanics.

Efficient Parallel Computer Simulation of the Motion Behaviors of Closed-Loop Multibody Systems

2007 ◽  
Author(s):  
Shanzhong Duan ◽  
Andrew Ries
Keyword(s):  
Parallel Computing ◽  
Multibody Systems ◽  
Closed Loop ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Parallel Computer ◽  
Constraint Forces ◽  
Computing Systems ◽  
Closed Loops

This paper presents an efficient parallelizable algorithm for the computer-aided simulation and numerical analysis of motion behaviors of multibody systems with closed-loops. The method is based on cutting certain user-defined system interbody joints so that a system of independent multibody subchains is formed. These subchains interact with one another through associated unknown constraint forces fc at the cut joints. The increased parallelism is obtainable through cutting joints and the explicit determination of associated constraint forces combined with a sequential O(n) method. Consequently, the sequential O(n) procedure is carried out within each subchain to form and solve the equations of motion while parallel strategies are performed between the subchains to form and solve constraint equations concurrently. For multibody systems with closed-loops, joint separations play both a role of creation of parallelism for computing load distribution and a role of opening a closed-loop for use of the O(n) algorithm. Joint separation strategies provide the flexibility for use of the algorithm so that it can easily accommodate the available number of processors while maintaining high efficiency. The algorithm gives the best performance for the application scenarios for n>>1 and n>>m, where n and m are number of degree of freedom and number of constraints of a multibody system with closed-loops respectively. The algorithm can be applied to both distributed-memory parallel computing systems and shared-memory parallel computing systems.

scholarly journals Proof of Lagrange's Equations of Motion, &c.

Nature ◽  
1903 ◽  
Vol 67 (1740) ◽  
pp. 415-415
Author(s):  
W. MCF. ORR
Keyword(s):  
Equations Of Motion ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

scholarly journals Proof of Lagrange's Equations of Motion, &c.

Nature ◽  
1903 ◽  
Vol 67 (1740) ◽  
pp. 415-415
Author(s):  
R. F. W.
Keyword(s):  
Equations Of Motion ◽  
Lagrange’S Equations ◽  
Lagrange's Equations

scholarly journals Finite Element Method-Based Elastic Analysis of Multibody Systems. A Review

Mathematics ◽  
2022 ◽  
Vol 10 (2) ◽  
pp. 257
Author(s):  
Sorin Vlase ◽  
Marin Marin ◽  
Negrean Iuliu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mechanical System ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Alternative Methods ◽  
Engineering Applications ◽  
Lagrange’S Equations ◽  
Lagrange's Equations ◽  
Element Method

This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

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