Class 5 Mechanical Systems (Both Translation and Rotational)

CONTROL
ENGINEERING
Sangamesh C M
Department of Mechanical
Engineering
CONTROL ENGINEERING
Introduction
Sangamesh C M
Department of Mechanical Engineering
Control Engineering
Introduction
UNIT:1 Introduction to automatic control system

Class 5
In this class you learn about Modelling of Mechanical systems
i.e. translational and rotational
Lesson Content
Concepts of
 Mechanical systems Translational

 Mechanical systems Rotational
Control Engineering
Introduction
Mechanical system
In the mechanical system, motion can be of different types i.e.,

Translational and rotational or combination of both. The
equations governing such motion in mechanical system are
often directly or indirectly governed by Newton's law of
motion
1. Translational mechanical systems
2. Rotational mechanical systems

Control Engineering
Introduction
Modeling of Translational Mechanical Systems
 Consider a mechanical system in which motion is taking

place along a straight line. Such systems are of translational
type.
 These systems are characterized by displacement, linear
velocity and linear acceleration.
 According to newton's, sum of forces applied on rigid body

or a system must be equal to sum of forces consumed to
produce displacement, velocity and acceleration.
Control Engineering
Introduction
Mass
 Mass is the property of the system itself, which stores kinetic

energy. If a force is applied on a body having mass M, then it
is opposed by an opposing force due to mass.
 The displacement of the mass always takes place in the

direction of the applied force.
 This is the property of the system itself which stores the
kinetic energy of the translation motion.
 Mass has no power to store the potential energy
 It measured in kilogram
Control Engineering
Introduction
Mass
 This opposing force is proportional to the acceleration of

the body. Assume elasticity and friction are negligible.
Control Engineering
Introduction
Mass equation
𝑑2 𝑥
𝐹 𝑡 = 𝑀 ∗ 𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 = 𝑀 2
𝑑𝑡
Taking Laplace and neglecting initial conditions we can write,

F(s) = Ms X(s)
Control Engineering
Introduction
Spring
 Spring is an element, which stores potential energy. If a
force is applied on spring K, then it is opposed by an
opposing force due to elasticity of spring.
 This opposing force is proportional to the displacement of

the spring. Assume mass and friction are negligible.
Control Engineering
Introduction
Spring equation
F(t) = K * x
Where,
F is the applied force
Fk------- is the opposing force due to elasticity of spring
K------ is spring constant
x------- is displacement
Control Engineering
Introduction
Dashpot
 If a force is applied on dashpot B, then it is opposed by an
opposing force due to friction of the dashpot.
 This opposing force is proportional to the velocity of the

body. Assume mass and elasticity are negligible.
Control Engineering
Introduction
Dashpot equation
F∝v
𝑑𝑥
F= B
𝑑𝑡
Where,
F --------- -is the opposing force due to friction of dashpot
B ----------- is the frictional coefficient
V ----------- is velocity
x ------------ is displacement
Control Engineering
Introduction
Modelling of Rotational Mechanical Systems

 Rotational mechanical systems move about a fixed axis.
These systems mainly consist of three basic elements. Those
are moment of inertia, torsional spring and dashpot.
 If a torque is applied to a rotational mechanical system, then

it is opposed by opposing torques due to moment of inertia,
elasticity and friction of the system.
 Since the applied torque and the opposing torques are in

opposite directions, the algebraic sum of torques acting on
the system is zero. Let us now see the torque opposed by
these three elements individually.
Control Engineering
Introduction
Moment of Inertia
 In translational mechanical system, mass stores kinetic

energy. Similarly, in rotational mechanical system, moment
of inertia stores kinetic energy.
 If a torque is applied on a body having moment of inertia J,

then it is opposed by an opposing torque due to the
moment of inertia.
Control Engineering
Introduction
Moment of Inertia
 This opposing torque is proportional to angular

acceleration of the body. Assume elasticity and friction are
negligible.
Control Engineering
Introduction
Moment of Inertia equation
T∝a
𝑑2 𝛳
T =J
𝑑𝑡 2
Where,
T ---------is the applied torque
J ---------is moment of inertia
a -------- is angular acceleration
Θ -------- is angular displacement
Control Engineering
Introduction
Torsional Spring
 In translational mechanical system, spring stores potential

energy. Similarly, in rotational mechanical system, torsional
spring stores potential energy.
 If a torque is applied on torsional spring K, then it is

opposed by an opposing torque due to the elasticity of
torsional spring.
Control Engineering
Introduction
Torsional Spring
 This opposing torque is proportional to the angular

displacement of the torsional spring. Assume that the
moment of inertia and friction are negligible.
Control Engineering
Introduction
Torsional Spring equation
T∝ϴ
T = Kϴ
T = Kϴ
Where,
T ----------is the applied torque
K --------- is the torsional spring constant
Θ ----------is angular displacement
Control Engineering
Introduction
Dashpot
 If a torque is applied on dashpot B, then it is opposed by an
opposing torque due to the rotational friction of the
dashpot.
 This opposing torque is proportional to the angular velocity

of the body. Assume the moment of inertia and elasticity
are negligible.
Control Engineering
Introduction
Dashpot equation is given by

T∝ὠ
𝑑𝛳
T= B
𝑑𝑡
Where,
T --------- rotational torque
B ---------- is the rotational friction coefficient
ω ----------is the angular velocity
θ -----------is the angular displacement
THANK YOU
Sangamesh C M
Department of Mechanical Engineering
sangameshm@pes.edu
+91 8073038517

Class 5 Mechanical Systems (Both Translation and Rotational)

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CONTROL

UNIT:1 Introduction to automatic control system

 Mechanical systems Translational

In the mechanical system, motion can be of different types i.e.,

1. Translational mechanical systems

2. Rotational mechanical systems

Modeling of Translational Mechanical Systems

 Consider a mechanical system in which motion is taking

 According to newton's, sum of forces applied on rigid body

 Mass is the property of the system itself, which stores kinetic

 The displacement of the mass always takes place in the

 This opposing force is proportional to the acceleration of

Taking Laplace and neglecting initial conditions we can write,

 This opposing force is proportional to the displacement of

 This opposing force is proportional to the velocity of the

Modelling of Rotational Mechanical Systems

 If a torque is applied to a rotational mechanical system, then

 Since the applied torque and the opposing torques are in

 In translational mechanical system, mass stores kinetic

 If a torque is applied on a body having moment of inertia J,

 This opposing torque is proportional to angular

Moment of Inertia equation

 In translational mechanical system, spring stores potential

 If a torque is applied on torsional spring K, then it is

 This opposing torque is proportional to the angular

Torsional Spring equation

 This opposing torque is proportional to the angular velocity

Dashpot equation is given by

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