Dynamic Modelling and Analysis of General Linked Mechanisms With Compliance

1987 ◽  
Author(s):  
L. Shih ◽  
A. A. Frank
Keyword(s):  
Equations Of Motion ◽  
Real Life ◽  
Dynamic Modelling ◽  
Joint Models ◽  
Kinematic Chains ◽  
3 Dimensional ◽  
Compliant Joint ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Joint Clearances

Abstract This paper presents a simple and systematic method of analysis for the kinematics and dynamics of spatial multi-loop mechanisms with closed and open kinematic chains. The Newton-Euler formulation is used to derive the dynamic equations of motion of each link. This formulation completely eliminates kinematic redundancies and singularities. Compliant joint models are introduced to cover real life effects such as joint clearances, lubrication of joints, joint to link compliances, etc. Direct computation of joint reaction forces results. An example of the application of the method to the dynamic and kinematic analysis of a 3 dimensional spatial slider-crank mechanism with a flywheel is presented.

Application of the Vector-Network Method to Constrained Mechanical Systems

1986 ◽  
Vol 108 (4) ◽  
pp. 471-480 ◽  
Author(s):  
Tai-Wai Li ◽  
Gordon C. Andrews
Keyword(s):  
Equations Of Motion ◽  
Mechanical Systems ◽  
Computer Applications ◽  
Kinematic Chains ◽  
Constrained Mechanical Systems ◽  
3 Dimensional ◽  
Methodical Approach ◽  
Dynamic Formulation ◽  
Reaction Forces ◽  
New Formulation

The vector-network technique is a methodical approach to formulating equations of motion for unconstrained dynamic systems, utilizing concepts from graph theory and vectorial mechanics; it is ideally suited to computer applications. In this paper, the vector-network theory is significantly improved and extended to include constrained mechanical systems with both open and closed kinematic chains. A new formulation procedure is developed in which new kinematic constraint elements are incorporated. The formulation is based on a modified tree/cotree classification, which deviates significantly from previous work, and reduces the number of equations of motions to be solved. The dynamic equations of motion are derived, with generalized accelerations and a subset of the reaction forces as solution variables, and a general kinematic analysis procedure is also developed, similar to that of the dynamic formulation. Although this paper restricts most discussions to two-dimensional (planar) systems, the new method is equally applicable to 3-dimensional systems.

Mechanism Analysis Using Implicit Constraints

2008 ◽  
Author(s):  
George H. Sutherland
Keyword(s):  
Equations Of Motion ◽  
Reaction Force ◽  
Mechanism Analysis ◽  
Kinematic Parameters ◽  
Joint Reaction Force ◽  
Dynamic Mechanisms ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Mechanism Kinematic ◽  
Joint Reaction

This paper introduces an approach to kinematic and dynamic mechanisms analysis where one or more joints are modeled using joint component relative displacements that approximate real joint behavior. This approach allows for the simultaneous nonrecursive solution for both mechanism kinematic parameters and selected dynamic joint reaction forces. Also, for closed loop mechanisms, the approach eliminates the need for forming explicit loop closure constraint equations, so that the dynamic equations of motion, derived using either the Newtonian or Lagrangian method, have a simplified unconstrained form. The key element underlying the approach is the formation of axioms for the standard mechanism joint types that describe the form of the joint reaction force and/or moment in terms of a virtual (or real) displacement between the joint components.

PROBABILISTIC BEHAVIOR OF JOINT FORCES IN MECHANISMS

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Boštjan Harl ◽  
Marko Kegl ◽  
Nenad Gubeljak ◽  
Dejan Dinevski
Keyword(s):  
Mining Industry ◽  
Hydraulic Support ◽  
Kinematic Chains ◽  
Taylor Approximation ◽  
The Monte Carlo Method ◽  
Joint Forces ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Joint Reaction ◽  
Actual Part

This paper discusses the influence of the clearance in joints on the joint reaction forces in mechanisms. By using mathematical programing, the optimal parameters of kinematic chains can be efficiently obtained by using the deterministic approach. However, the situation becomes more sophisticated if random effects of tolerances of the arm lengths and the random pin positions have to be considered. In this work the influence of clearances on joint forces is calculated by using the Taylor approximation and the Monte Carlo method. Using the two methods was necessary, because the Taylor approximation usually yields satisfying results only for small values of clearances and for this reason it makes sense to compute the required quantities also by another independent method. The implementation of the model is illustrated with two examples. The first example considers a closed loop chain, representing a four-bar mechanism being an actual part of a hydraulic support, employed in mining industry. The hydraulic support must fulfill some requirements so it’s very important to have influence of clearances on joint forces in control. The second example considers joint reaction forces of car wiper mechanism. It will be shown, that the clearance in joints have some influence on the joint reaction forces.

Computational Analysis of Multibody Dynamic Systems Using Nonlinear Recursive Formulation

2009 ◽  
Vol 419-420 ◽  
pp. 289-292
Author(s):  
Yunn Lin Hwang ◽  
Shen Jenn Hwang ◽  
Zi Gui Huang ◽  
Ming Tzong Lin ◽  
Yen Chien Mao ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Recursive Formulation ◽  
Loosely Coupled ◽  
Multibody Dynamic ◽  
Joint Coordinates ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Strong Dynamic ◽  
Joint Reaction

. In this paper the computer implementation of the nonlinear recursive formulation in multibody dynamics systems is described. The organization of the computer algorithm which is used to automatically construct and numerically solve the system of loosely coupled dynamic equations expressed in terms of the absolute and joint coordinates is discussed. The inertia projection schemes used in most existing recursive formulations for the dynamic analysis of deformable mechanisms lead to dense coefficient matrices in the equations of motion. Consequently, there are strong dynamic couplings between the joint and elastic coordinates. By using the inertia matrix structure of deformable mechanical systems and the fact that the joint reaction forces associated with the elastic coordinates do represent independent variables, a reduced system of equations whose dimension is dependent of the number of elastic degrees of freedom is obtained. This system can be solved for the joint accelerations as well as the joint reaction forces. The multibody flexible four-bar system is used as an example to demonstrate the use of the procedure discussed in this paper.

scholarly journals Minimization of dynamic joint reaction forces of the 2-DOF serial manipulators based on interpolating polynomials and counterweights

2015 ◽  
Vol 42 (4) ◽  
pp. 249-260 ◽  
Author(s):  
Slavisa Salinic ◽  
Marina Boskovic ◽  
Radovan Bulatovic
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Lagrange Equations ◽  
Symbolic Form ◽  
Serial Manipulators ◽  
Joint Reaction Forces ◽  
Reaction Forces ◽  
Inertia Forces ◽  
Joint Reaction ◽  
Selection Of

This paper presents two ways for the minimization of joint reaction forces due to inertia forces (dynamic joint reaction forces) in a two degrees of freedom (2-DOF) planar serial manipulator. The first way is based on the optimal selection of the angular rotations laws of the manipulator links and the second one is by attaching counterweights to the manipulator links. The influence of the payload carrying by the manipulator on the dynamic joint reaction forces is also considered. The expressions for the joint reaction forces are obtained in a symbolic form by means of the Lagrange equations of motion. The inertial properties of the manipulator links are represented by dynamical equivalent systems of two point masses. The weighted sum of the root mean squares of the magnitudes of the dynamic joint reactions is used as an objective function. The effectiveness of the two ways mentioned is discussed.

Effect of Variation of Link Lengths and Stiffness on the Gearing Ratio of a Four Bar Mechanism With Application to Aircraft Trim Tabs

2015 ◽  
Author(s):  
Abey Dessalegn ◽  
Yimesker Yihun ◽  
Joao Paulo Flores Fernandes ◽  
Hamid M. Lankarani
Keyword(s):  
Rigid Body ◽  
Closed Form ◽  
Real Life ◽  
Algebraic Solution ◽  
End Effector ◽  
Mechanical Advantage ◽  
Kinematic Chains ◽  
Joint Clearances

Kinematic chains or mechanisms have conventionally been analyzed comprising of links that behave as rigid members and links assumed to be built at nominal sizes. Such mechanisms, articulating entirely from rigid-body translations and/or rotations and nominally established links may not closely represent the actual real life manufactured parts with tolerances and joint clearances. It is important to identify the allowable variations in the linkages especially when the end-effector of the mechanism generates a path or a function and/or a tightly controlled gearing ratio or mechanical advantage is required. In this study, the band of solutions that can be obtained from the variation in lengths of linkages and the effect of stiffness is generated to better understand the quality of the mechanism performance. The application of four bar mechanism in an aileron trim tab system that utilizes a rotatory actuator to move the tab surface is used to demonstrate the band of solutions. Then CATIA V5 is used to layout the geometry and design the linkages within the prescribed airfoil. The MSC Adams is used to calculate the initial gearing ratio and for validation of values. A Matlab®code is developed and used to analyze the effects of the variation of lengths and stiffness of linkages on the tab speed using closed form algebraic solution. Finally, a comparison is made to illustrate and quantify the effects of link lengths and stiffness on the gearing ratio/mechanical advantage of the system.

Recursive Dynamics of Overconstrained Mechanisms

1994 ◽  
Author(s):  
Udo Rein
Keyword(s):  
Closed Loop ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Open Loop ◽  
Loop Closure ◽  
Kinematic Chains ◽  
Reaction Forces ◽  
Overconstrained Mechanisms ◽  
Recursive Dynamics ◽  
Closure Constraints

Abstract Overconstrained mechanisms contain loop-closure constraints which are redundant due to a special geometry of the links. Some reaction forces of an overconstrained mechanism cannot be calculated from the dynamics of the mechanism. This means that an overconstrained mechanism is statically indeterminate. The recursive formalism was originally developed to derive the equations of motion for open-loop kinematic chains, but it has been extended by various authors to closed-loop mechanisms. This paper discusses the recursive formalism when it is applied to an overconstrained closed-loop mechanism. It will be shown that the redundant loop-closure constraints lead to rather small singular, but consistent sets of linear equations for the reaction forces at the corresponding cut joints. This means that the reaction forces at those cut joints are not unique for an overconstrained mechanism, but the variety of possible solutions does not affect the dynamics of the overconstrained mechanism. This behaviour of the recursive formalism can be used to perform an on-line investigation of the static indeterminacy of a mechanism, including singular positions, where joint constraints are redundant only at one specific position.

Knee Joint Loading During Lineman-Specific Movements in American Football Players

2015 ◽  
Vol 31 (3) ◽  
pp. 142-148 ◽  
Author(s):  
Rebecca L. Lambach ◽  
Jay W. Young ◽  
David C. Flanigan ◽  
Robert A. Siston ◽  
Ajit M.W. Chaudhari
Keyword(s):  
Inverse Dynamics ◽  
Cartilage Damage ◽  
American Football ◽  
3 Dimensional ◽  
Increase Risk ◽  
Joint Reaction Forces ◽  
Cartilage Injuries ◽  
Univariate Anova ◽  
Reaction Forces ◽  
Joint Reaction

Linemen are at high risk for knee cartilage injuries and osteoarthritis. High-intensity movements from squatting positions (eg, 3-point stance) may produce high joint loads, increasing the risk for cartilage damage. We hypothesized that knee moments and joint reaction forces during lineman-specific activities would be greater than during walking or jogging. Data were collected using standard motion analysis techniques. Fifteen NCAA linemen (mean ± SD: height = 1.86 ± 0.07 m, mass = 121.45 ± 12.78 kg) walked, jogged, and performed 3 unloaded lineman-specific blocking movements from a 3-point stance. External 3-dimensional knee moments and joint reaction forces were calculated using inverse dynamics equations. MANOVA with subsequent univariate ANOVA and post hoc Tukey comparisons were used to determine differences in peak kinetic variables and the flexion angles at which they occurred. All peak moments and joint reaction forces were significantly higher during jogging than during all blocking drills (all P < .001). Peak moments occurred at average knee flexion angles > 70° during blocking versus < 44° in walking or jogging. The magnitude of moments and joint reaction forces when initiating movement from a 3-point stance do not appear to increase risk for cartilage damage, but the high flexion angles at which they occur may increase risk on the posterior femoral condyles.

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