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ME 311: Dynamics of Machines and

Mechanisms

Lecture 4: Dynamics Fundamentals

By

Suril Shah

Mechanical Department

IIT Jodhpur

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Kinematics Vs. Dynamics

KINEMATICS: The study of motion without regard to forces.

Aim is to Create the desired motions

Compute the positions, velocities, accelerations

DYNAMICS (Kinetics): The study of forces on systems in motion.

Aim is to Creating systems which will not fail during their expected

service life

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Law 1

Every body preserves in its state of rest or of motion in a straight line, except in so far as it is compelled to change

that state by impresses forces.

A Modified form:

If all the forces acting on a particle are balanced, the particle will either remain at rest or will continue to move

in a straight line at a uniform velocity

Statics

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Law 2

Change of motion is proportional to the moving force impressed, and takes place in the directions of the straight line in which such force is impresses

A Modified form:

If the forces acting on a particle are not balanced, the particle will experience an acceleration proportional to the resultant force and in the direction of the resultant force.

Dynamics

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Law 3

Reaction is always equal and opposite to action: that is to say, the action of two bodies upon each other are always equal and directly opposite.

A Modified form:

When two particles react, a pair of interacting forces come into existence; these forces have the same magnitude and opposite sense, and they act along the straight line common to the two particle.

Constraint forces

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Dynamic Analysis

Force analysis: Forces under the application of joint motion

Inverse Dynamics Driving forces: Control

Constraint forces: Design

Motion analysis: Configuration of the linkages under forces

Forward Dynamics Simulation , performance evaluation

Mathematical

model

ForceMotion

Pelvis Joints

Motion Force

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DYNAMIC MODELS

Simplified model of a complicated part

A collection of point masses connected by massless rods.

A rigid body is dynamically equivalent to the original body The mass of the model must equal that of the original

body.

The center of gravity must be in the same location as that of the original body.

The mass moment of inertia must equal that of the original body.

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Dynamics: Equations of motion

Study of forces and moments causing the motion in a

system.

Equation of motion (Newtons second law of motion )

Mass (m)Force (f) Motion (a)

= aCM

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Mass

Resistance to change in linear motion

f = maCM

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Mass Moment

(first moment of mass)

Mass Moment of diff. mass =

Product of its mass and its

distance from the axis of

interest.

With respect to the x, y, and z

axes these are: The mass moments of the body

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R. L. Norton, 2004

Centre of Mass (CM)

What is If the mass moment wrt to an axis is zero?

The axis passes through the CM

Hence, CM is calculated by equating

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R. L. Norton, 2004

= 0

= 0

= 0

CM of Complicated shape

Divide into simple shapes whose

CM are known.

Global CM is found as

Summation of the first moments of

these simple shapes set equal to zero.

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https://images.google.com/

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An example

= 0

= 0

=

=

=

http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html

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An example

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R. L. Norton, 2004

Mass moment of Inertia

(Second moment)

Rotational form of Newton's second law is:

T = I

Moment of inertia is a measure of

resistance to angular acceleration.

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Mass moment of Inertia Moment of inertia of the

diff. element = product of its mass and the square of its distance from the axis of interest.

With respect to the X, Y, and Z axes they are:

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Mass moments of inertia of

the body

R. L. Norton, 2004

Physical Significance: Mass moment of

Inertia (I) I is proportional to the square of the radius from

the axis of rotation

Takes considerably more torque to swing the hammer when it is held properly than if held near the head.

Why is it ineffective in driving nails when held close to the head?

Because you were unable to store very much kinetic energy in it.

kinetic energy for rotating system

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https://images.google.com/

Design considerations

Ability of the body to store rotational kinetic energy

Indicator of the amount of torque that will be needed to rotationally accelerate the body.

Try to minimize the moments of inertia of your rotating parts

Exception: device intended for the storage and transfer of large amounts of energy (punch press, drop hammer, rock crusher etc.)

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Practical Session on ADAMS

Session 1 (90 minutes): ADAMS Introduction

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Practical Session on ADAMS

Session 2 (90 minutes):

Simulation of Klann

mechanism shown in the

first figure.

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https://www.youtube.com/watch?v=XFBUUrkGtQM

THANK YOU

Questions?

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