• Journal of the Korean Society for Precision Engineering
• /
• v.22 no.4
• /
• pp.128-135
• /
• 2005

Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

• International Journal of Precision Engineering and Manufacturing
• /
• v.2 no.4
• /
• pp.61-68
• /
• 2001

A new approach for motion control of constrained mechanical systems is proposed in this paper. The approach uses a new equations of motion which is proposed by Udwadia and Kalaba and named Udwadia-Kalaba's equations of motion in this paper. This paper reveals that the Udwadia-Kalaba's equations of motion is more adequate to model constrained mechanical systems rather than the famous Lagrange's equations of motion at least for control purpose. The proposed approach coverts most of constraints including holonomic and nonholonomic constraints. Comparison of simulation results of two systems which are well-known in the literature show the superiority of the proposed approach. Furthermore, a special constrained mechanical system which includes nonlinear generalized velocities in its constraint equations, which has been considered to be difficult to control, can be controlled easily. It shows the possibility of the proposed approach to being a general framework for motion control of constrained mechanical systems with various kinds of constraints.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10a
• /
• pp.926-930
• /
• 1993

An efficient method of formulating the equations of motion of multibody systems is presented. The equations of motion for each body are formulated by using Newton-Eulerian approach in their generic form. And then a transformation matrix which relates the global coordinates and relative coordinates is introduced to rewrite the equations of motion in terms of relative coordinates. When appropriate set of kinematic constraints equations in terms of relative coordinates is provided, the resulting differential and algebraic equations are obtained in a suitable form for computer implementation. The system geometry or topology is effectively described by using the path matrix and reference body operator.

• East Asian mathematical journal
• /
• v.37 no.2
• /
• pp.265-288
• /
• 2021

In the 2015 revised mathematics curriculum, the system of equations is first introduced in 'Variables and Expressions' of [Middle School Grades 1-3]. Then, It is constructed that after learning the linear function in 'Functions', the relationship between the graphs of two linear functions and the systems of linear equations are learned so that students could improve the geometric representation of the systems of equations. However, in of Elective-Centered Curriculum Common Courses, Instruction is limited to algebraic manipulation when teaching and learning systems of quadratic equations. This paper presented the teaching and learning method that can improve students' mathematical connection through various representations by providing geometric representations in parallel using GeoGebra, a mathematics learning software, with algebraic solutions in the teaching and learning situation of simultaneous quadratic equations.

• Journal of Mechanical Science and Technology
• /
• v.17 no.4
• /
• pp.538-544
• /
• 2003

Although many methodologies exist for determining the constrained equations of motion, most of these methods depend on numerical approaches such as the Lagrange multiplier's method expressed in differential/algebraic systems. In 1992, Udwadia and Kalaba proposed explicit equations of motion for constrained systems based on Gauss's principle and elementary linear algebra without any multipliers or complicated intermediate processes. The generalized inverse method was the first work to present explicit equations of motion for constrained systems. However, numerical integration results of the equation of motion gradually veer away from the constraint equations with time. Thus, an objective of this study is to provide a numerical integration scheme, which modifies the generalized inverse method to reduce the errors. The modified equations of motion for constrained systems include the position constraints of index 3 systems and their first derivatives with respect to time in addition to their second derivatives with respect to time. The effectiveness of the proposed method is illustrated by numerical examples.

• Journal of Educational Research in Mathematics
• /
• v.17 no.2
• /
• pp.91-109
• /
• 2007

This study deals with the problem of transition from arithmetic to algebra and the relationship between elementary and secondary school mathematics for systems of linear equations. In elementary school, activity for solving word problems related to systems of linear equations in two variables falls broadly into using two strategies: Guess and check and making a table. In secondary school, those problems are solved algebraically, for example, by solving systems of equations using the technique of elimination. The analysis of mathematics textbooks shows that there is no link between strategies of elementary school mathematics and secondary school mathematics. We devised an alternative way to reinforce link between elementary and secondary school mathematics for systems of linear equations. Drawing a diagram can be introduced as a strategy solving word problems related to systems of linear equations in two variables in elementary school. Moreover it is closely related to the idea of the technique of elimination of secondary school mathematics. It may be a critical juncture of elementary-secondary school mathematics in the case of systems of linear equations in two variables.

• Journal of applied mathematics & informatics
• /
• v.15 no.1_2
• /
• pp.285-297
• /
• 2004

The general scheme of an algorithm, called an ABS-FRE algorithm, for solving systems of fuzzy relation equations (systems of FRE) via the ABS algorithms is presented. As special cases, two particular algorithms for obtaining the greatest and minimal solutions of systems of FRE are described. Several new operations used in this scheme are given, for instance, operators $\veebar$ and $\underline{\wedge}$ called quasi-inverses of operators $\vee$ and $\wedge$, respectively, etc.

• Journal of KSNVE
• /
• v.7 no.5
• /
• pp.773-780
• /
• 1997

Using Generalized Inverse Method presented by Udwadia and Kalaba in 1992, we can obtain equations to exactly describe the motion of constrained systems. When the differential equations are numerically integrated by any numerical integration scheme, the numerical results are generally found to veer away from satisfying constraint equations. Thus, this paper deals with the numerical integration of the differential equations describing constrained systems. Based on Baumgarte method, we propose numerical methods for reducing the errors in the satisfaction of the constraints.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.9
• /
• pp.2339-2348
• /
• 1994

The objective of this paper is to develop a solution method for the differential-algebraic equation(DAE) derived from constrained muti-body dynamic systems. Mechanical systems are often modeled as bodies and joints. Differential equations of motion are formulated for bodies. Since the bodies are connected by joint, the differential variables must satisfy the kinematic constraint equations that come from the joints. Difficulties are arised due to drift of the differential variables off the constraint equations. An optimization method is adopted to correct the drift of the differential variables. To demonstrate the efficiency of the proposed method a slider-crank mechanism is analyzed dynamically. Identical results are obtained as these from the commercial program DADS. Dynamic analysis of a High Mobility Multi-purpose Wheeled. Vehicle(HMMWV) is carried out to show the practicalism of the proposed method.

• Structural Engineering and Mechanics
• /
• v.5 no.2
• /
• pp.209-220
• /
• 1997

The dynamic equations for an arbitrary cluster comprising rigid spheres or assemblies of spheres (subclusters) encountered in granular-type systems are considered. The system is treated within the framework of multibody dynamics. It is shown that for an arbitrary cluster topology the governing equations can be given in an explicit scalar from. The derivation is based on the D'Alembert principle, on inertial coordinate system for each body and direct utilization of the path matrix describing the topology. The scalar form of the equations is important in computer simulations of flow of granular-type materials. An illustrative example of a three-body system is given.