Page 91 - The Mechatronics Handbook

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7

Modeling Electro-

mechanical Systems

7.1 Introduction
7.2 Models for Electromechanical Systems
7.3 Rigid Body Models
Kinematics of Rigid Bodies • Constraints and Generalized
Coordinates • Kinematic versus Dynamic Problems
7.4 Basic Equations of Dynamics of Rigid Bodies
Newton–Euler Equation • Multibody Dynamics
7.5 Simple Dynamic Models
Compound Pendulum • Gyroscopic Motions
7.6 Elastic System Modeling
Piezoelastic Beam
7.7 Electromagnetic Forces
7.8 Dynamic Principles for Electric
and Magnetic Circuits
Lagrange’s Equations of Motion for Electromechanical Systems
Francis C. Moon 7.9 Earnshaw’s Theorem and Electromechanical
Cornell University Stability

7.1 Introduction

Mechatronics describes the integration of mechanical, electromagnetic, and computer elements to pro-
duce devices and systems that monitor and control machine and structural systems. Examples include
familiar consumer machines such as VCRs, automatic cameras, automobile air bags, and cruise control
devices. A distinguishing feature of modern mechatronic devices compared to earlier controlled machines
is the miniaturization of electronic information processing equipment. Increasingly computer and elec-
tronic sensors and actuators can be embedded in the structures and machines. This has led to the need
for integration of mechanical and electrical design. This is true not only for sensing and signal processing
but also for actuator design. In human size devices, more powerful magnetic materials and supercon-
ductors have led to the replacement of hydraulic and pneumatic actuators with servo motors, linear
motors, and other electromagnetic actuators. At the material scale and in microelectromechanical systems
(MEMS), electric charge force actuators, piezoelectric actuators, and ferroelectric actuators have made
great strides.
While the materials used in electromechanical design are often new, the basic dynamic principles of
Newton and Maxwell still apply. In spatially extended systems one must solve continuum problems using
the theory of elasticity and the partial differential equations of electromagnetic field theory. For many
applications, however, it is sufficient to use lumped parameter modeling based on i) rigid body dynamics

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