Kinematics of Machinery - Introduction

INTRODUCTION

Kinematics: The study of motion without regard to forces.

Kinetics: The study of forces on systems in motion.

DIAGRAM SHOWING LATHE PARTS

THE SHAPER

Number of links, L = 12,

12 11

10

98

7

6

5

1

2

3

4

11, 12

1

2

3

4

56

78

9

10

Mechanism: A system of elements arranged to transmit motion in a predetermined fashion.

Machine : A system of elements arranged to transmit motion and energy in a predetermined fashion.

Mechanism can also be defined as a device that transforms motion to some desirable pattern and typically develops very low forces and transmits little power.

Virtually any machine or device that moves contains one or more kinematic elements such as links, gears, cams, belts, chains.

Mechanism: A combination of no. of bodies (usually resistant bodies) assembled in such a way that the motion of one causes constrained and predictable motion to the others is known as a mechanism.

A mechanism is made of no. of resistant bodies out of which some have relative to the others.

Link: A resistant body or a group of resistant bodies (with no relative motion among them) of a mechanism, connecting other members and having motion relative to them is called a kinematic link.

(or)

A link is a rigid body that possesses at least 2 nodes that are points of attachment to other links

Types:

1. Binary link – 2nodes2. Ternary link3. Quaternary link

Kinematic pair: A kinematic pair or simply a pair is a joint of 2 links having relative motion between them.

Classification: Based on

1. Nature of contact : Lower and higher pairs

2. Nature of Mechanical constraint : Closed and unclosed pair

3. Nature of relative motion

4. No. of DOF

Based on nature of relative motion:

Based on nature of mechanical constarint:1. Closed pair or form closed pair2. Unclosed pair or force closed pair

Kinematic chain:

A Kinematic chain is an assembly of links in which the relative motion of the links is possible and the motion of each relative to the other is definite.

Linkage

Mechanism

Kinematic chain:

A Kinematic chain is an assembly of links in which the relative motion of the links is possible and the motion of each relative to the other is definite.

Linkage: If one of the links of a KC is fixed to the ground

Mechanism: If motion of any one of the links results in definite motion of the others.

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Surface contact pairs are lower pairs.

The commonly used lower pairs include

(1) Revolute Pair

(2) Prismatic Pair

(3) Screw Pair

(4) Cylindrical Pair

(5) Spherical Pair

(6) Planar Pair

LOWER KINEMATIC PAIRS

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Degrees of freedom: 1 Symbol: P Relative motion: linear

PRISMATIC PAIR (SLIDER JOINT)

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Degrees of freedom: 1 Symbol: H Relative motion: Helical

SCREW PAIR (HELICAL PAIR)

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Degrees of freedom: 2 Symbol: C Relative motion: Cylindrical

CYLINDRICAL PAIR

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Degrees of freedom: 3 Symbol: S Relative motion: Spherical

SPHERICAL PAIR (GLOBULAR PAIR)

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Degrees of freedom: 3 Symbol: F Relative motion: Planar

PLANAR PAIR (FLAT PAIR)

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Higher pairs (joints) have either a line contact or a  point contact.

Higher pairs exist in cam mechanisms, gear trains, ball and roller bearings and roll-slide joints, etc.

For planar motion, both line contact higher pairs and point contact higher pairs have two degrees-of-freedom.

The only constraint at the contact point is along the common normal.

A pin-in-slot joint (rolling contact with sliding) is also a higher pair with a line contact between the pin and the slot.

HIGHER KINEMATIC PAIRS

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HIGHER KINEMATIC PAIRS

higher.SLDASM

Linkage: If one of the links of a KC is fixed to the ground

Mechanism: If motion of any one of the links results in definite motion of the others.

Degrees of freedom

General defn: The DOF of a body is equal to the no. of independent coordinates required to specify its position.

Spatial D.O.F. Planar D.O.F.

R – Pair P – Pair C - Pair

For a Link – Six in spatial motion, three in planar motion.

For a Kinematic Pair –

Number of independent co-ordinates/pair variables to specify the position of one link with another link

(OR)

Number of independent relative motions possible between the links. Maximum five and minimum one in spatial motion. Maximum two and minimum one in planar motion.

Kinematic chain:

A Kinematic chain is an assembly of links in which the relative motion of the links is possible and the motion of each relative to the other is definite.

A closed chain is a consecutive set of links in which the last link is connected to the first.

An open chain is the one in which the last link is not connected to the first link.

A closed chain mechanism. An open chain

mechanism.

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KINEMATIC CHAIN CLOSED

5 bar linkage.SLDASM

Ground

Slider-crank

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KINEMATIC CHAIN OPEN

fanuc robot.SLDASM

Ground

Degrees of freedom/Mobility of a mechanism

• No. of inputs required to get a constrained mechanism (or) no. of position variables needed to sketch the mechanism with all link lengths known.

Ken Youssefi Mechanical & Aerospace Engineering Dept., SJSU

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DEGREES OF FREEDOM (DOF)

Kutzbach’s (modified Grubler) equation

DOF ≤ 0 structure

mechanismDOF > 0

• F = 3(n-1)-2P1-1P2

• F – D.O.F n – No. of links

• P1 – No. of kinematic pairs with 1 D.O.F.

• P2 – No. of kinematic pairs with 2 D.O.F.

Exception’s