A Recursive Dynamic Formulation for Flexible Mechanisms

1990 ◽  
Author(s):  
Byung Yil Souh ◽  
S. S. Kim
Keyword(s):  
Equations Of Motion ◽  
Mode Selection ◽  
Nonlinear Effects ◽  
Body Motion ◽  
Flexible Link ◽  
Open Chain ◽  
Closed Loop Systems ◽  
Dynamic Formulation ◽  
Nodal Coordinates ◽  
Assumed Mode

Abstract This paper presents a recursive dynamic formulation for modeling and simulation of spatial mechanisms with elastic beams. In order to circumvent some difficulties in the convential assumed mode approach, each flexible link is modeled with finite elements. The motion of the flexible link comprises the rigid body motion and elastic deformation. The elastic deformations are represented by nodal coordinates relative to the moving coordinate system fixed to the link. Recursive kinematic relationships are derived between finite beam elements. Using variational equations of motion for the one beam element and recursive relationships, the equations of motion for the open-chain flexible bodies are derived in terms of relative joint and nodal coordinates. For closed-loop systems, Lagrange multipliers are used to generate the equations of motion with kinematic constraints. The proposed method models geometric nonlinear effects and axial tensioning effects automatically. Also, the difficulties of the mode selection in the assumed mode approach is avoided. Numerical examples illustrate the effectiveness of this approach.

Steady-State Responses of an RSRC-Type Spatial Flexible Linkage

1994 ◽  
Vol 116 (1) ◽  
pp. 264-269 ◽  
Author(s):  
R. Y. Chang ◽  
C. K. Sung
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Body Motion ◽  
Flexible Link ◽  
Predictive Capability ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Steady State Responses ◽  
State Responses ◽  
Flexible Linkage

This paper presents an analytical and experimental investigation on the steady-state responses of an RSRC-type spatial flexible linkage. The kinematic analysis of the spatial rigid-body motion is performed using kinematic constraint equations to yield the linear and angular positions, velocities, and accelerations of the linkage. A mixed variational principle is, then, employed to derive the equations of motion governing the longitudinal, transverse, and torsional vibrations of the flexible link and the associated boundary conditions. Based on these equations, the steady-state responses are predicted. Finally, an RSRC-type four-bar spatial flexible linkage is constructed and the experimental study is performed to examine the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

Steady-State Responses of an RSRC-Type Spatial Flexible Linkages

1992 ◽  
Author(s):  
R. Y. Chang ◽  
C. K. Sung
Keyword(s):  
Steady State ◽  
Equations Of Motion ◽  
Body Motion ◽  
Flexible Link ◽  
Predictive Capability ◽  
Kinematic Constraint ◽  
Constraint Equations ◽  
Steady State Responses ◽  
State Responses ◽  
Flexible Linkage

Abstract This paper presents an analytical and experimental investigation on the steady-state responses of an RSRC-type spatial flexible linkage. The kinematic analysis of the spatial rigid-body motion is performed using kinematic constraint equations to yield linear and angular positions, velocities and accelerations of the linkage. A mixed variational principle is, then, employed to derive the equations of motion governing the longitudinal, transversal and torsional vibrations of the flexible link and the associated boundary conditions. Based on these equations, the steady-state responses are predicted. Finally, an RSRC-type four-bar spatial flexible linkage is constructed and the experimental study is performed to examine the predictive capability proposed in this investigation. Favorable comparisons between the analytical and experimental results are obtained.

Using Nonlinear Recursive Formulation for the Kinematic Analysis of Human Biomechanical Systems

2012 ◽  
Vol 482-484 ◽  
pp. 938-941
Author(s):  
Yunn Lin Hwang ◽  
Wei Hsin Gau ◽  
Wen Huang Lin ◽  
Shen Jenn Hwang ◽  
Chien Hsin Chen
Keyword(s):  
Kinematic Analysis ◽  
Equations Of Motion ◽  
Open Loop ◽  
Body Motion ◽  
Displacement Fields ◽  
Flexible Bodies ◽  
Recursive Formulation ◽  
Closed Loop Systems ◽  
Generalized Newton ◽  
Time Invariant

Generally speaking, the human biomechanical systems can be classified into two main groups: open-loop and closed-loop systems. In this investigation, the nonlinear recursive formulation is developed for the kinematic analysis of human biomechanical systems. The nonlinear generalized Newton-Euler equations are developed for flexible bodies that undergo large translational and rotational displacements. These equations are formulated in terms of a set of time invariant scalars, vectors and matrices that depend on the spatial coordinates as well as the assumed displacement fields, and these time invariant quantities represent the dynamic coupling between the rigid body motion and elastic deformation. The formulation to solve equations of motion for human biomechanical systems consisting of interconnected rigid and flexible bodies is presented in this paper.

scholarly journals Use of mixed coordinates in modeling wind turbines including tubular tower

2019 ◽  
Vol 10 (1) ◽  
pp. 35-46
Author(s):  
Ayman Nada ◽  
Ali Al-Shahrani
Keyword(s):  
Wind Turbine ◽  
Equations Of Motion ◽  
Body Motion ◽  
Computational Time ◽  
Proposed Model ◽  
Nodal Model ◽  
Nodal Coordinates ◽  
Mixed Coordinates ◽  
Modal Coordinates ◽  
Turbine Model

Abstract. This paper studies the effect of the tower dynamics upon the wind turbine model by using mixed sets of rigid and/or nodal and/or modal coordinates within multibody system dynamics approach. The nodal model exhibits excellent numerical properties, especially in the case where the rotation of the rotor-blade is extremely high, and therefore, the geometric stiffness effect can not be ignored. However, the use of nodal models to describe the flexibility of large multibody systems produces huge size of coordinates and may consume massive computational time in simulation. On the other side, the dynamics of the tower as well as other components of wind turbine remain exhibit small deformations and can be modeled using Cartesian and/or reduced set of modal coordinates. The paper examines a method of using mixed sets of different coordinates in the same model, although there are differences in the scale and the physical interpretation. The equations of motion of the wind-turbine model is presented based on the floating frame of reference formulation. The mixed coordinates vector consists of three sets: Cartesian coordinates set to present the rigid body motion (nacelle and rotor bodies), elastic nodal coordinates for rotating blades, and reduced-order modal coordinates for low speed components and those that deflect by simple motion shapes (circular Tower). Experimental validation has been carried out successfully, and consequently, the proposed model can be utilized for design process, identification and health monitoring aspects.

scholarly journals Vibration Analysis of a New Type of Compliant Mechanism with Flexible-Link, Using Perturbation Theory

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
N. S. Viliani ◽  
H. Zohoor ◽  
M. H. Kargarnovin
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Vibration Analysis ◽  
Compliant Mechanism ◽  
Equations Of Motion ◽  
Mode Shapes ◽  
Flexible Link ◽  
Assumed Mode Method ◽  
New Type ◽  
Assumed Mode

Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange’s equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with Runge-Kutta-Fehlberg 4, 5th leads to highly accurate solutions, and the results are performed and discussed.

Human Motion Modeling With a Robotics Method: Analysis of a Person Riding a Bus

2008 ◽  
Author(s):  
Ashish D. Deshpande ◽  
Jonathan E. Luntz
Keyword(s):  
Equations Of Motion ◽  
Human Motion ◽  
Contact Forces ◽  
Body Motion ◽  
Control Analysis ◽  
Motion Modeling ◽  
Open Chain ◽  
Motion Models ◽  
Performance Requirements ◽  
And Control

Deriving models of human body motion is important for prosthetics, rehabilitation and development of humanoids. We present a method that simplifies the derivation of equations of motion of human movements. We illustrate our approach by deriving motion models of a person riding in a moving bus. Our approach simplifies the derivation of dynamics as only open chain dynamics are to be derived. The kinematic constraints are then introduced to represent a complete system model in which the contact forces appear explicitly. We then constrain the contact forces based on the performance requirements to determine the feasibility of motions, which is difficult to determine with the traditional methods. Our model allows for the design and control analysis, specifically, the derivation of the relationship between the change in rider’s posture and the feasibility of motions.

Exact Modeling of the Spatial Rigid Body Inertia Using the Finite Element Method

1998 ◽  
Vol 120 (3) ◽  
pp. 650-657 ◽  
Author(s):  
A. P. Christensen ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Rigid Body ◽  
Coordinate System ◽  
Deformable Body ◽  
Equations Of Motion ◽  
Body Motion ◽  
Intermediate Element ◽  
Nodal Coordinates ◽  
Body Inertia ◽  
Isoparametric Elements

In the classical finite element literature beams and plates are not considered as isoparametric elements since infinitesimal rotations are used as nodal coordinates. As a consequence, exact modeling of an arbitrary rigid body displacement cannot be obtained, and rigid body motion does not lead to zero strain. In order to circumvent this problem in flexible multibody simulations, an intermediate element coordinate system, which has an origin rigidly attached to the origin of the deformable body coordinate system and has axes which are parallel to the axes of the element coordinate system in the undeformed configuration was introduced. Using this intermediate element coordinate system and the fact that conventional beam and plate shape functions can describe an arbitrary rigid body translation, an exact modeling of the rigid body inertia can be obtained. The large rigid body translation and rotational displacements can be described using a set of reference coordinates that define the location of the origin and the orientation of the deformable body coordinate system. On the other hand, as demonstrated in this investigation, the incremental finite element formulations do not lead to exact modeling of the spatial rigid body mass moments and products of inertia when the structures move as rigid bodies, and such formulations do not lead to the correct rigid body equations of motion. The correct equations of motion, however, can be obtained if the coordinates are defined in terms of global slopes. Using this new definition of the element coordinates, an absolute nodal coordinate formulation that leads to a constant mass matrix for the element can be developed. Using this formulation, in which no infinitesimal or finite rotations are used as nodal coordinates, beam and plate elements can be treated as isoparametric elements.

Some Nonlinear Effects of Magnetic Bearings

1999 ◽  
Author(s):  
Norbert Steinschaden ◽  
Helmut Springer
Keyword(s):  
Equations Of Motion ◽  
Period Doubling ◽  
Path Following ◽  
Nonlinear Effects ◽  
Magnetic Bearing ◽  
Operating Conditions ◽  
Active Magnetic Bearing ◽  
Nonlinear Phenomena ◽  
Amb System ◽  
Large Rotor

Abstract In order to get a better understanding of the dynamics of active magnetic bearing (AMB) systems under extreme operating conditions a simple, nonlinear model for a radial AMB system is investigated. Instead of the common way of linearizing the magnetic forces at the center position of the rotor with respect to rotor displacement and coil current, the fully nonlinear force to displacement and the force to current characteristics are used. The AMB system is excited by unbalance forces of the rotor. Especially for the case of large rotor eccentricities, causing large rotor displacements, the behaviour of the system is discussed. A path-following analysis of the equations of motion shows that for some combinations of parameters well-known nonlinear phenomena may occur, as, for example, symmetry breaking, period doubling and even regions of global instability can be observed.

The Global Motion of a Rigid Body Subject to Periodic Body-Fixed Torques

1995 ◽  
Author(s):  
X. Tong ◽  
B. Tabarrok
Keyword(s):  
Rigid Body ◽  
Equations Of Motion ◽  
Melnikov Method ◽  
The Body ◽  
Body Motion ◽  
Heteroclinic Orbits ◽  
Coordinate Frame ◽  
Global Motion ◽  
Stable And Unstable Manifolds ◽  
Body Subject

Abstract In this paper the global motion of a rigid body subject to small periodic torques, which has a fixed direction in the body-fixed coordinate frame, is investigated by means of Melnikov’s method. Deprit’s variables are introduced to transform the equations of motion into a form describing a slowly varying oscillator. Then the Melnikov method developed for the slowly varying oscillator is used to predict the transversal intersections of stable and unstable manifolds for the perturbed rigid body motion. It is shown that there exist transversal intersections of heteroclinic orbits for certain ranges of parameter values.

On the Properties of a Dynamic Model of Flexible Robot Manipulators

1998 ◽  
Vol 120 (1) ◽  
pp. 8-14 ◽  
Author(s):  
Marco A. Arteaga
Keyword(s):  
Dynamic Model ◽  
Structural Properties ◽  
Robot Manipulators ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Control Design ◽  
Flexible Manipulator ◽  
Robot Dynamics ◽  
Flexible Link ◽  
Flexible Robot

Control design of flexible robot manipulators can take advantage of the structural properties of the model used to describe the robot dynamics. Many of these properties are physical characteristics of mechanical systems whereas others arise from the method employed to model the flexible manipulator. In this paper, the modeling of flexible-link robot manipulators on the basis of the Lagrange’s equations of motion combined with the assumed modes method is briefly discussed. Several notable properties of the dynamic model are presented and their impact on control design is underlined.

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