Inverse Static Analysis of a Planar System With Flexural Pivots

2000 ◽  
Vol 123 (1) ◽  
pp. 43-50 ◽  
Author(s):  
Marco Carricato ◽  
Vincenzo Parenti-Castelli ◽  
Joseph Duffy
Keyword(s):  
Static Analysis ◽  
External Load ◽  
Degrees Of Freedom ◽  
Linear Functions ◽  
State Variables ◽  
Special Design ◽  
Planar System ◽  
Planar Mechanism ◽  
Equilibrium Configurations ◽  
Solving Equations

This article presents the inverse static analysis of a two degrees of freedom planar mechanism with flexural pivots. Such analysis aims to detect the entire set of equilibrium configurations of the system once the external load is assigned. The presence of flexural pivots represents a novelty, although it remarkably complicates the problem since it causes the two state variables to appear in the solving equations as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention is paid to the analysis of the reliability of the final equations: critical situations, in which the solving equations may hide solutions or yield false ones, are studied. Finally, a numerical example is provided and, in the Appendix, a special design that offers computational advantages is proposed.

Inverse Static Analysis of a Planar System With Spiral Springs

2000 ◽  
Author(s):  
Marco Carricato ◽  
Joseph Duffy ◽  
Vincenzo Parenti-Castelli
Keyword(s):  
Static Analysis ◽  
External Load ◽  
Degrees Of Freedom ◽  
The Other ◽  
Linear Functions ◽  
State Variables ◽  
Planar System ◽  
Equilibrium Configurations ◽  
Solving Equations ◽  
The One

Abstract In this article the inverse static analysis of a two degrees of freedom planar mechanism equipped with spiral springs is presented. Such analysis aims to detect the entire set of equilibrium configurations of the mechanism once the external load is assigned. While on the one hand the presence of flexural pivots represents a novelty, on the other it extremely complicates the problem, since it brings the two state variables in the solving equations to appear as arguments of both trigonometric and linear functions. The proposed procedure eliminates one variable and leads to write two equations in one unknown only. The union of the root sets of such equations constitutes the global set of solutions of the problem. Particular attention has been reserved to the analysis of the “reliability” of the final equations: it has been sought the existence of critical situations, in which the solving equations hide solutions or yield false ones. A numerical example is provided. Also, in Appendix it is shown a particular design of the mechanism that offers computational advantages.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

scholarly journals Trajectory Planning of Manipulator Using Optimization of Uniform B-Spline

1994 ◽  
Vol 6 (6) ◽  
pp. 491-498 ◽  
Author(s):  
Hiroaki Ozaki ◽  
◽  
Hua Chiu ◽  
Keyword(s):  
Trajectory Planning ◽  
Degrees Of Freedom ◽  
Control Points ◽  
State Variables ◽  
B Spline ◽  
Iterative Computation ◽  
Basic Optimization ◽  
Engineering Problems ◽  
Original Objective ◽  
Optimum Solution

A basic optimization algorithm is presented in this paper, in order to obtain the optimum solution of a two-point boundary value variational problem without constraints. The solution is given by a parallel and iterative computation and described as a set of control points of a uniform B-spline. This algorithm can also be applied to solving problems with some constraints, if we introduce an additional component, namely the potential function, corresponding to constraints in the original objective function. The algorithm is very simple and easily applicable to various engineering problems. As an application, trajectory planning of a manipulator with redundant degrees of freedom is considered under the conditions that the end effector path, the smoothness of movement, and the constraints of the control or the state variables are specified. The validity of the algorithm is well confirmed by numerical examples.

A multi-configuration kinematic model for active drive/steer four-wheel robot structures

Robotica ◽  
2015 ◽  
Vol 34 (10) ◽  
pp. 2309-2329 ◽  
Author(s):  
Edgar A. Martínez-García ◽  
Erik Lerín-García ◽  
Rafael Torres-Córdoba
Keyword(s):  
Degrees Of Freedom ◽  
Rotation Axis ◽  
Contact Point ◽  
Linear Equations ◽  
Kinematic Model ◽  
Robotic Systems ◽  
Control Law ◽  
Special Design ◽  
Wheel Drive ◽  
Four Wheel Drive

SUMMARYIn this study, a general kinematic control law for automatic multi-configuration of four-wheel active drive/steer robots is proposed. This work presents models of four-wheel drive and steer (4WD4S) robotic systems with all-wheel active drive and steer simultaneously. This kinematic model comprises 12 degrees of freedom (DOFs) in a special design of a mechanical structure for each wheel. The control variables are wheel yaw, wheel roll, and suspension pitch by active/passive damper systems. The pitch angle implies that a wheel's contact point translates its position over time collinear with the robot's lateral sides. The formulation proposed involves the inference of the virtual z-turn axis (robot's body rotation axis) to be used in the control of the robot's posture by at least two acceleration measurements local to the robot's body. The z-turn axis is deduced through a set of linear equations in which the number of equations is equal to the number of acceleration measurements. This research provides two main models for stability conditions. Finally, the results are sustained by different numerical simulations that validate the system with different locomotion configurations.

A Vector Bond Graph Method of Kineto-Static Analysis for Spatial Multibody Systems

2013 ◽  
Vol 321-324 ◽  
pp. 1725-1729 ◽  
Author(s):  
Zhong Shuang Wang ◽  
Yang Yang Tao ◽  
Quan Yi Wen
Keyword(s):  
Static Analysis ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Multibody System ◽  
Graph Model ◽  
Bond Graph ◽  
Constraint Forces ◽  
Decoupling Method ◽  
Complete Form ◽  
Three Degrees Of Freedom

In order to increase the reliability and efficiency of the kineto-static analysis of complex multibody systems, the corresponding vector bond graph procedure is proposed. By the kinematic constraint condition, spatial multibody systems can be modeled by vector bond graph. For the algebraic difficulties brought by differential causality in system automatic kineto-static analysis, the effective decoupling method is proposed, thus the differential causalities in system vector bond graph model can be eliminated. In the case of considering EJS, the unified formulae of driving moment and constraint forces at joints are derived based on vector bond graph, which are easily derived on a computer in a complete form and very suitable for spatial multibody systems. As a result, the automatic kineto-static analysis of spatial multibody system on a computer is realized, its validity is illustrated by the spatial multibody system with three degrees of freedom.

A Unified Framework for Dynamics and Lyapunov Stability of Holonomically Constrained Rigid Bodies

2005 ◽  
Vol 9 (4) ◽  
pp. 387-394 ◽  
Author(s):  
Khoder Melhem ◽  
◽  
Zhaoheng Liu ◽  
Antonio Loría ◽  
◽  
...  
Keyword(s):  
System Dynamics ◽  
Lyapunov Stability ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Minimal Realization ◽  
State Variables ◽  
Unified Framework ◽  
Constrained System ◽  
And Control

A new dynamic model for interconnected rigid bodies is proposed here. The model formulation makes it possible to treat any physical system with finite number of degrees of freedom in a unified framework. This new model is a nonminimal realization of the system dynamics since it contains more state variables than is needed. A useful discussion shows how the dimension of the state of this model can be reduced by eliminating the redundancy in the equations of motion, thus obtaining the minimal realization of the system dynamics. With this formulation, we can for the first time explicitly determine the equations of the constraints between the elements of the mechanical system corresponding to the interconnected rigid bodies in question. One of the advantages coming with this model is that we can use it to demonstrate that Lyapunov stability and control structure for the constrained system can be deducted by projection in the submanifold of movement from appropriate Lyapunov stability and stabilizing control of the corresponding unconstrained system. This procedure is tested by some simulations using the model of two-link planar robot.

A Three-Dimensional Dynamic Model for Determining the Equilibrium Configurations of Buoyantly Unstable Icebergs

1990 ◽  
Vol 112 (3) ◽  
pp. 253-262
Author(s):  
R. G. Jessup ◽  
S. Venkatesh
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Static Potential ◽  
Initial State ◽  
Model Simulations ◽  
Six Degrees Of Freedom ◽  
Equilibrium Configurations ◽  
Variation Range

This paper describes a dynamic model developed for the purpose of determining the final equilibrium configurations of buoyantly unstable icebergs. The model places no restrictions on the size, shape, or dimensionality of the iceberg, or on the variation range of the configuration coordinates. Furthermore, it includes all six degrees of freedom and is based on a Lagrangian formulation of the dynamic equations of motion. It can be used to advantage in those situations in which the iceberg has a complicated potential function and can acquire enough momentum and kinetic energy in the initial phase of its motion to make its final configuration uncertain on the basis of a static potential analysis. The behavior of the model is examined through several model simulations. The sensitivity of the final equilibrium position to the initial orientation and shape of the iceberg is clearly evident in the model simulations. Model simulations also show that when an iceberg is released from a nonequilibrium initial state, the time taken for it to settle down varies from about 40 s for a growler to nearly 400 s for a large iceberg. While these absolute times may change with better parameterization of the forces, the relative variations with iceberg size are likely to be preserved.

On the Static Stability Analysis of Viscoelastic Perfect Columns

1985 ◽  
Vol 9 (3) ◽  
pp. 157-164
Author(s):  
W. Szyszkowski ◽  
P.G. Glockner
Keyword(s):  
Stability Analysis ◽  
Static Analysis ◽  
Element Model ◽  
Static Stability ◽  
Model Material ◽  
Zero Eigenvalue ◽  
Equilibrium Configurations ◽  
Static Approach ◽  
Elastic Column ◽  
New Interpretation

In this article the direct static equilibrium approach for stability analysis is used to study the behaviour of a perfect column made of a linear three-element model material and subjected to a concentric load. The study confirms that such a traditional static analysis admits only one non-zero eigenvalue, namely the load a the instant of application, referred to as the Euler load, PE, for the corresponding elastic column. A new interpretation of adjacent equilibrium configurations for viscoelastic structures is introduced which permits an ‘exact’ static analysis of the problem. The results from this analysis agree, in part, with those obtained from a general dynamic stability analysts. They help to clear up some misinterpretations resulting from the application of the static approach and show that time, being inherently an asymmetric parameter, generates effects typical of asymmetric influences and decreases the critical load of the structure.

Flexible-Body Dynamics Modelling With a Reduced-Order Model

1990 ◽  
Author(s):  
K. Harold Yae ◽  
Daniel J. Inman
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Reduced Model ◽  
Flexible Body ◽  
State Variables ◽  
Dynamics Modeling ◽  
Element Analysis ◽  
Stiffness Matrices

Abstract In the dynamics modeling of a flexible body, finite element analysis employs Guyan’s reduction that removes some of the “insignificant” physical coordinates, thus producing a dynamic model that has smaller mass and stiffness matrices. Despite such reduction, the resultant model is still too large for flexible-body dynamic analysis. That warrants further reduction as is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. When the reduced model is being assembled with other bodies in a multi-body mechanism, a problem, however, arises because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, we developed a method that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this stage, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed in this paper, however, this reduced model is expressed by a subset of the original states. Then finally the model can be represented by the states assigned to the degrees of freedom of the selected nodal points.

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