Motivating Kane's method for obtaining equations of motion for dynamic systems

1989 ◽  
Vol 12 (4) ◽  
pp. 593-595 ◽  
Author(s):  
Joel Storch ◽  
Stephen Gates
Keyword(s):  
Dynamic Systems ◽  
Equations Of Motion ◽  
Kane’S Method ◽  
Kane's Method

Dynamics Modeling of Elastic Multibody Systems Using Kane’s Method As Applied to a Flexible Robot

1997 ◽  
Author(s):  
Ali Meghdari ◽  
Farbod Fahimi
Keyword(s):  
Multibody Systems ◽  
Equations Of Motion ◽  
Component Mode Synthesis ◽  
Flexible Robot ◽  
Dynamics Modeling ◽  
Generalized Coordinates ◽  
Kane’S Method ◽  
Kane's Method ◽  
Elastic Multibody Systems ◽  
Elastic Form

Abstract Generalization of Kane’s equations of motion for elastic multibody systems is considered. Initially, finite element techniques are used to generate the elastic form of generalized coordinates. Then, the number of elastic coordinates are reduced by the component mode synthesis. Finally, Kane’s method is applied to obtain the equations of motion of such systems. Using this method, dynamic model of an elastic robot with one degree of freedom is presented.

Dynamical Equations With Non-Ideal Constraints: New and Old Alternatives

2007 ◽  
Author(s):  
Arun K. Banerjee ◽  
Mark Lemak
Keyword(s):  
Equations Of Motion ◽  
Alternative Form ◽  
Constraint Forces ◽  
Dynamical Equations ◽  
Constraint Force ◽  
Kane’S Method ◽  
Kane's Method ◽  
Ellipsoidal Surface ◽  
Ideal Constraint ◽  
The Ideal

This paper deals with the motion of mechanical systems with non-ideal constraints, defined as constraints where the forces associated with the constraint do work. The first objective of the paper is to show that two newly published formulations of equations of motion of systems with such non-ideal constraints are unnecessarily complex for situations where the non-ideal constraint force does not depend on the ideal constraint force, because they introduce and then eliminate these non-working constraint forces. We point out that a method already exists for nonideal constraints, namely, Kane’s equations, which are simpler because, among other things, they are based on automatic elimination of non-working constraints. The examples considered in these recent publications are worked out with Kane’s method to show the applicability and simplicity of Kane’s method for non-ideal constraints. A second objective of the paper is to present an alternative form of equations for systems where the non-ideal constraint force depends on the ideal constraint force, as in the case of Coulomb friction. The formulation is shown to lend itself naturally to also analyzing impact dynamics. The method is applied to the dynamics of a slug moving against friction on a moving ellipsoidal surface. Such a crude model may simulate, in essence, propellant motion in a tank in zero-g, or during docking of a spacecraft.

Comparison of Kane’s and Lagrange’s Methods in Analysis of Constrained Dynamical Systems

Robotica ◽  
2020 ◽  
Vol 38 (12) ◽  
pp. 2138-2150
Author(s):  
Amin Talaeizadeh ◽  
Mahmoodreza Forootan ◽  
Mehdi Zabihi ◽  
Hossein Nejat Pishkenari
Keyword(s):  
Dynamical Systems ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Constrained Systems ◽  
Robot Dynamics ◽  
Energy Error ◽  
Kane’S Method ◽  
Kane's Method ◽  
Constrained Dynamical Systems ◽  
Error Energy

SUMMARYDynamic modeling is a fundamental step in analyzing the movement of any mechanical system. Methods for dynamical modeling of constrained systems have been widely developed to improve the accuracy and minimize computational cost during simulations. The necessity to satisfy constraint equations as well as the equations of motion makes it more critical to use numerical techniques that are successful in decreasing the number of computational operations and numerical errors for complex dynamical systems. In this study, performance of a variant of Kane’s method compared to six different techniques based on the Lagrange’s equations is shown. To evaluate the performance of the mentioned methods, snake-like robot dynamics is considered and different aspects such as the number of the most time-consuming computational operations, constraint error, energy error, and CPU time assigned to each method are compared. The simulation results demonstrate the superiority of the variant of Kane’s method concerning the other ones.

A geometrical interpretation of Kane’s Equations

1992 ◽  
Vol 436 (1896) ◽  
pp. 69-87 ◽  
Keyword(s):  
Tangent Space ◽  
Equations Of Motion ◽  
Rigid Bodies ◽  
Analytical Mechanics ◽  
Kane’S Method ◽  
Kane's Method ◽  
Kane’S Equations ◽  
Kane's Equations ◽  
Spanning Set ◽  
Geometric Picture

The method for the development of the equations of motion for systems of constrained particles and rigid bodies, developed by T. R. Kane and called Kane’s Equations, is discussed from a geometric viewpoint. It is shown that what Kane calls partial velocities and partial angular velocities may be interpreted as components of tangent vectors to the system’s configuration manifold. The geometric picture, when attached to Kane’s formalism shows that Kane’s Equations are projections of the Newton-Euler equations of motion onto a spanning set of the configuration manifold’s tangent space. One advantage of Kane’s method, is that both non-holonomic and non-conservative systems are easily included in the same formalism. This easily follows from the geometry. It is also shown that by transformation to an orthogonal spanning set, the equations can be diagonalized in terms of what Kane calls the generalized speeds. A further advantage of the geometric picture lies in the treatment of constraint forces which can be expanded in terms of a spanning set for the orthogonal complement of the configuration tangent space. In all these developments, explicit use is made of a concrete realization of the multidimensional vectors which are called K -vectors for a K -component system. It is argued that the current presentation also provides a clear tutorial route to Kane’s method for those schooled in classical analytical mechanics.

scholarly journals Motions of a Constrained Spherical Pendulum in an Arbitrarily Moving Reference Frame: The Automobile Seatbelt Inertial Sensor

1995 ◽  
Vol 2 (3) ◽  
pp. 227-236 ◽  
Author(s):  
A. Peter Allan ◽  
Miles A. Townsend
Keyword(s):  
Numerical Simulation ◽  
Reference Frame ◽  
Inertial Sensor ◽  
Equations Of Motion ◽  
Sensor Design ◽  
Spherical Pendulum ◽  
Crash Data ◽  
Kane’S Method ◽  
Kane's Method ◽  
Automobile Crash

A common automatic seatbelt inertial sensor design, comprised of a constrained spherical pendulum, is modeled to study its motions and possible unintentional release during vehicle emergency maneuvers. The kinematics are derived for the system with the most general inputs: arbitrary pivot motions. The influence of forces due to gravity and constraint torque functions is developed. The equations of motion are then derived using Kane's method. The equations of motion are used in a numerical simulation with both actual and hypothetical automobile crash data.

scholarly journals Use of Kane’s Method for Multi-Body Dynamic Modelling and Control of Spar-Type Floating Offshore Wind Turbines

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6635
Author(s):  
Saptarshi Sarkar ◽  
Breiffni Fitzgerald
Keyword(s):  
Wind Turbine ◽  
Equations Of Motion ◽  
Dynamic Modelling ◽  
Offshore Wind ◽  
Offshore Wind Turbine ◽  
Kane’S Method ◽  
Kane's Method ◽  
Floating Offshore Wind Turbines ◽  
Multi Body ◽  
And Control

This paper demonstrates the use of Kane’s method to derive equations of motion for a spar-type floating offshore wind turbine taking into account the flexibility of the members. The recently emerged Kane’s method reduces the effort required to derive equations of motion for complex multi-body systems, making them simpler to model and more readily solved by computers. Further, the installation procedure of external vibration control devices on the wind turbine using Kane’s method is described, and the ease of using this method has been demonstrated. A tuned mass damper inerter (TMDI) is installed in the tower for illustration. The excellent vibration mitigation properties of the TMDI are also presented in this paper.

scholarly journals Applying Kane’s Method to Model the Response of the Human Body to Whole-Body Vibration

2014 ◽  
Author(s):  
Emma Gantzer ◽  
Shanzhong (Shawn) Duan ◽  
Teresa Binkley
Keyword(s):  
Human Body ◽  
Equations Of Motion ◽  
Whole Body Vibration ◽  
Rigid Bodies ◽  
Skeletal Structure ◽  
Whole Body ◽  
Mineral Density ◽  
Body Vibration ◽  
Kane’S Method ◽  
Kane's Method

Low magnitude, high frequency whole-body vibration (WBV) has been found to increase bone mineral density in both animal and clinical studies [1,2,3]. The mechanism behind this phenomenon is unknown and a model would be beneficial to assist in analyzing the effects of WBV on the human skeleton. In this paper, Kane’s method is used to find the equations of motion for a multi-body model of the human body standing on a vibration platform [4]. The model consists of nine rigid bodies connected by ideal joints that simulate the skeletal structure of the human body. Spring and damper elements represent the ligaments and tendons connecting the rigid bodies; a sinusoidal force function denotes the vibration input of the platform. This model is lumped, assuming no relative motion between the feet and the vibration platform. The equations of motion generated by Kane’s method are solved in MATLAB using fourth-order Runge-Kutta. The results from the simulation were compared to experimental data in order to validate the model.

Characterization of Dynamics in Special 6-6 PKMs

2000 ◽  
Author(s):  
Scott A. Shamblin ◽  
Gloria J. Wiens
Keyword(s):  
Machine Tools ◽  
Equations Of Motion ◽  
Kane’S Method ◽  
Kane's Method ◽  
Parallel Kinematic ◽  
Parallel Kinematic Mechanisms ◽  
Kinematic Mechanisms

Abstract This paper presents a study on the contributions of the dynamics on the performance of a special 6-6 parallel kinematic mechanisms, with application to machine tools. Using Kane’s method, the dynamics equations of motion are derived with inclusion of the strut masses. Comparative observations are made using both workspace and sample trajectory based characterizations.

Multibody Dynamics: A Formulation Using Kane’s Method and Dual Vectors

1993 ◽  
Vol 115 (4) ◽  
pp. 833-838 ◽  
Author(s):  
S. K. Agrawal
Keyword(s):  
Multibody Dynamics ◽  
Multibody Systems ◽  
Nonholonomic System ◽  
Equations Of Motion ◽  
Nonholonomic Systems ◽  
Dynamic Equations ◽  
Kane’S Method ◽  
Kane's Method ◽  
Holonomic Systems ◽  
Holonomic And Nonholonomic Systems

This paper proposes a formulation based on Kane’s method to form the dynamic equations of motion of multibody systems using dual vectors. Both holonomic and nonholonomic systems are considered in this formulation. An example of a holonomic and a nonholonomic system is worked out in detail using this formulation. This algorithm is shown to be advantageous for a class of holonomic systems which has cylindrical joints.

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