Dynamic Force Analysis of Spatial Linkages

1967 ◽  
Vol 34 (2) ◽  
pp. 418-424 ◽  
Author(s):  
J. J. Uicker
Keyword(s):  
Dynamic Force ◽  
Force Analysis ◽  
Lagrange Equations ◽  
Single Degree Of Freedom ◽  
Digital Computation ◽  
Mass Distributions ◽  
Single Degree ◽  
The Matrix ◽  
Spatial Linkages ◽  
Matrix Expression

The matrix method of linkage analysis is extended to the analysis of the bearing forces and torques which result from the inertia of the moving links when a single-loop, single-degree-of-freedom linkage is driven with known input velocity and acceleration. The method is well suited to digital computation and has been tested on several examples of spatial linkages, one of which is presented. A 4 × 4 “inertia matrix” is defined to describe the mass distributions of the links, and a matrix expression is derived for their kinetic energy. The dynamic bearing reactions are found by using the Lagrange equations with a varying constraint.

Synthesizing Single DOF Linkages Via Transition Linkage Identification

2007 ◽  
Vol 130 (2) ◽  
Author(s):  
Andrew P. Murray ◽  
Michael L. Turner ◽  
David T. Martin
Keyword(s):  
Classification Scheme ◽  
Degree Of Freedom ◽  
Physical Parameters ◽  
Single Degree Of Freedom ◽  
Loop Closure ◽  
Single Degree ◽  
The Matrix ◽  
Comprehensive Classification ◽  
Insight Into ◽  
Selection Of

A linkage is partially classified by identifying those links capable of unceasing and drivable rotation and those that are not. In this paper, we examine several planar single degree-of-freedom linkages to identify all changes to the physical parameters that may alter this classification. The limits on the physical parameters that result in no change in the classification are defined by transition linkages. More rigorously, a transition linkage possesses a configuration at which the matrix defined by the derivative of the loop closure equations with respect to the joint variables loses rank. Transition linkages divide the set of all linkages into different classifications. In the simplest cases studied, transition linkage identification produces a comprehensive classification scheme. In all cases, this identification is used to alter a linkage’s physical parameters without changing its classification and produces insight into the selection of these parameters to produce a desired classification.

Branch Identification of Spherical Six-Bar Linkages

2016 ◽  
Author(s):  
Liangyi Nie ◽  
Jun Wang ◽  
Kwun-Lon Ting ◽  
Daxing Zhao ◽  
Quan Wang ◽  
...  
Keyword(s):  
Range Of Motion ◽  
Degree Of Freedom ◽  
Joint Rotation ◽  
Single Degree Of Freedom ◽  
Complex Issue ◽  
Single Degree ◽  
Identification Method ◽  
Spatial Linkages ◽  
Spherical Linkages

Branch (assembly mode or circuit) identification is a way to assure motion continuity among discrete linkage positions. Branch problem is the most fundamental, pivotal, and complex issue among the mobility problems that may also include sub-branch (singularity-free) identification, range of motion, and order of motion. Branch and mobility complexity increases greatly in spherical or spatial linkages. This paper presents the branch identification method suitable for automated motion continuity rectification of a single degree-of-freedom of spherical linkages. Using discriminant method and the concept of joint rotation space (JRS), the branch of a spherical linkage can be easily identified. The proposed method is general and conceptually straightforward. It can be applied for all linkage inversions. Examples are employed to illustrate the proposed method.

A Describing Function for Dynamic Forces in Single Degree-of-Freedom Mechanisms

1980 ◽  
Vol 102 (4) ◽  
pp. 240-246
Author(s):  
R. R. Allen ◽  
D. M. Rozelle
Keyword(s):  
Degree Of Freedom ◽  
Dynamic Force ◽  
Inertial Effects ◽  
Time Domain Simulation ◽  
Describing Function ◽  
Spectral Content ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Dynamic Forces ◽  
Generalized Force

In a single degree-of-freedom mechanism, a generalized force is produced by elastic, dissipative, and inertial effects. This force may be expressed as a power series in the mechanism’s generalized velocity where the coefficients are functions of the generalized displacement. Approximating the coefficients by their Fourier series expansions produces a describing function which is rapidly convergent and provides substantial computational and analytical advantages over using the exact equations. This describing function permits efficient time-domain simulation of mechanism dynamics and produces an analytical expression for the spectral content of the mechanism dynamic force. Generation and application of the describing function is illustrated by a numerical example.

Dynamic Behavior of Spatial Linkages: Part 1—Exact Equations of Motion, Part 2—Small Oscillations About Equilibrium

1969 ◽  
Vol 91 (1) ◽  
pp. 251-265 ◽  
Author(s):  
J. J. Uicker
Keyword(s):  
Differential Equations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Dynamic Force ◽  
Lagrange Equations ◽  
Oscillation Analysis ◽  
Restricted Problems ◽  
The Matrix ◽  
Laplace Transformations ◽  
External Forces

Part 1: Over the past several years, the matrix method of linkage analysis has been developed to give the kinematic, static and dynamic force, error, and equilibrium analyses of three-dimensional mechanical linkages. This two-part paper is an extension of these methods to include some aspects of dynamic analysis. In Part 1, expressions are developed for the kinetic and potential energies of a system consisting of a multiloop, multi-degree-of-freedom spatial linkage having springs and damping devices in any or all of its joints, and under the influence of gravity as well as time varying external forces. Using the Lagrange equations, the exact differential equations governing the motion of such a system are derived. Although these equations cannot be solved directly, they form the basis for the solution of more restricted problems, such as a linearized small oscillation analysis which forms Part 2 of the paper. Part 2: This paper is a direct extension of Part 1 and it is assumed that the reader has a thorough knowledge of the previous material. Assuming that the spatial linkage has a stable position of static equilibrium and oscillates with small displacements and small velocities about this position, the general differential equations of motion are linearized to describe these oscillations. The equations lead to an eigenvalue problem which yields the resonant frequencies and associated damping constants of the system for the equilibrium position. Laplace transformations are then used to solve the linearized equations. Digital computer programs have been written to lest these methods and an example solution dealing with a vehicle suspension is presented.

Laguerre Series Solutions of the Delayed Single Degree-of-Freedom Oscillator Excited by an External Excitation and Controlled by a Control Force

2018 ◽  
Vol 15 (2) ◽  
pp. 606-610 ◽  
Author(s):  
Nurcan Baykuş Savaşaneril
Keyword(s):  
Laguerre Polynomials ◽  
Degree Of Freedom ◽  
Control Force ◽  
Numerical Application ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Laguerre Series ◽  
Analysis Technique ◽  
The Matrix ◽  
Fundamental Systems

With increasing technologies, applications of delayed models are more frequently encountered in biology, physics and various fields of engineering. The single degree-of-freedom oscillator, on the other hand, is one of the fundamental systems in many physics and engineering problems; thus, solving the equation of this problem would serve for many other sophisticated problems. In this study, a novel and simple numerical method for the solution of this system is introduced in the matrix form based on Laguerre polynomials. The method is exemplified through a numerical application and the results obtained are compared with those of another method. In addition, an error analysis technique based on residual function is developed and applied to this problem to demonstrate the validity and applicability of the method. The convenience of the method is that it is quite simple to employ by using computer programs.

scholarly journals A cross-species neural integration of gravity for motor optimization

2021 ◽  
Vol 7 (15) ◽  
pp. eabf7800
Author(s):  
Jeremie Gaveau ◽  
Sidney Grospretre ◽  
Bastien Berret ◽  
Dora E. Angelaki ◽  
Charalambos Papaxanthis
Keyword(s):  
Optimization Strategy ◽  
Motor Patterns ◽  
Activation Patterns ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Neural Integration ◽  
Gravity Effects ◽  
Neural Signature ◽  
Experimental Findings ◽  
Muscular Activation

Recent kinematic results, combined with model simulations, have provided support for the hypothesis that the human brain shapes motor patterns that use gravity effects to minimize muscle effort. Because many different muscular activation patterns can give rise to the same trajectory, here, we specifically investigate gravity-related movement properties by analyzing muscular activation patterns during single-degree-of-freedom arm movements in various directions. Using a well-known decomposition method of tonic and phasic electromyographic activities, we demonstrate that phasic electromyograms (EMGs) present systematic negative phases. This negativity reveals the optimal motor plan’s neural signature, where the motor system harvests the mechanical effects of gravity to accelerate downward and decelerate upward movements, thereby saving muscle effort. We compare experimental findings in humans to monkeys, generalizing the Effort-optimization strategy across species.

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