unit-i - kom slides.pdf

7/30/2019 Unit-I - KOM Slides.pdf

1/43

Types of Constrained Motions

Completely constrained motion

Incompletely constrained motion

Successfully constrained motion


2/43

Completely constrained motion


3/43

Incompletely constrained motion


4/43

Successfully constrained motion


5/43

According to the type of relativemotion between the elements

Sliding pair

Turning pair

Cylindrical pair Rolling pair

Spherical pair

Helical pair or screw pair


6/43


(a) Sliding pair [DOF = 1]

(b) Turning pair (revolute pair)[DOF = 1]


7/43


(c) Cylindrical pair [DOF = 2]

(d) Rolling pair [DOF = 1]


8/43


(e) Spherical pair [DOF = 3]

Eg. Ball and socket joint

(f) Helical pair or screw pair

[DOF = 1]


9/43

According to the type ofcontact between the elements

Lower pair

Higher pair


10/43

Lower pair

The joint by which two members areconnected has surface contact.


11/43

Higher pair

The contact between the pairing elementstakes place at a point or along a line.


12/43

According to the type of closure

(a) Self closed pair

(b) Force closed pair


13/43

Kinematic Chain

Group of links either joined together orarranged in a manner that permits them

to move relative to one another.


14/43

Locked Chain or Structure

Links connected in such a way that norelative motion is possible.


15/43

Types of Joints in a Chain

Binary joint

Ternary joint

Quaternary joint


16/43

locked / kinematic / unconstrainedchain

In order to determine the nature of chain, i.e.whether the chain is a locked chain (or structure)or kinematic chain or unconstrained chain, thefollowing relation between the number of links

and the number of binary joints, as given byA.W. Klein, may be used :


17/43


18/43

Kutzbach criterion for movability

A mechanism with l number oflinks connected byj numberofbinary joints or lower pairs (i.e. single degree of freedompairs) and h number ofhigher pairs (i.e. two degree offreedom pairs), then the number of degrees of freedom of amechanism is given by

If there are no two degree of freedom pairs (i.e. higher

pairs), then h = 0, we have


19/43

Application of Kutzbach Criterionto Plane Mechanisms


20/43

Grublers Criterion for PlaneMechanisms

The Grublers criterion applies to mechanismswith only single degree of freedom joints wherethe overall movability of the mechanism is unity.

Substituting n = 1 and h = 0 in Kutzbachequation, we have


21/43

Mechanism

A mechanism is a constrained kinematicchain. Motion of any one link in the

kinematic chain will give a definite andpredictable motion relative to each of theothers. Usually one of the links of thekinematic chain is fixed in a mechanism.


22/43

Types of Kinematic Chains

Four bar chain or quadric cyclic chain

Single slider crank chain

Double slider crank chain


23/43

Four bar chain or quadric cyclic chain

AB (link 1) which is fixed isknown as frame.

AD (link 4 ) make a completerevolution relative to the otherthree links is known as crank ordriver.

BC (link 2) which makes a partialrotation or oscillates is known aslever or rocker or follower.

CD (link 3) which connects thecrank and lever is calledconnecting rod or coupler.


24/43


25/43

Inversion of Mechanism

A mechanism is one in which one of thelinks of a kinematic chain is fixed.Different mechanisms can be obtained byfixing different links of the same kinematicchain. These are called as inversions ofthe mechanism.


26/43

Inversions of Four Bar Chain

Beam engine

(crank and lever mechanism)

Coupling rod of a locomotive

(Double crank mechanism)

Watts indicator mechanism

(Double lever mechanism)


27/43

Beam engine(crank and lever mechanism)


28/43

Coupling rod of a locomotive(Double crank mechanism)


29/43

Watts indicator mechanism(Double lever mechanism)


30/43

Single Slider Crank Chain

links 1 and 2, links 2 and 3, and links 3 and 4 form threeturning pairs

links 4 and 1 form a sliding pair.


31/43

Inversions of slider crank chain

(a) crank fixed (b) connecting rod fixed (c) slider fixed


32/43

Inversions of Single SliderCrank Chain

Pendulum pump or Bull engine

Oscillating cylinder engine

Rotary internal combustion engine

or Gnome engine

Crank and slotted lever quick returnmotion mechanism

Whitworth quick return motionmechanism


33/43

Pendulum pump or Bull engine


34/43

Oscillating cylinder engine


35/43

Rotary internal combustion engineor Gnome engine


36/43

Crank and slotted lever quickreturn motion mechanism


37/43

Crank and slotted lever quickreturn motion mechanism


38/43

Whitworth quick return motionmechanism


39/43

Double Slider Crank Chain

A kinematic chain whichconsists of two turningpairs and two sliding pairsis known as double slidercrank chain

link 2 and link 1 form oneturning pair.

link 2 and link 3 form thesecond turning pair.

link 3 and link 4 form onesliding pair.

link 1 and link 4 form thesecond sliding pair.


40/43

Inversions of Double SliderCrank Chain

Elliptical trammels

Scotch yoke mechanism

Oldhams coupling


41/43

Elliptical trammels

It is an instrument used for drawing ellipses.


42/43

Scotch yoke mechanism

This mechanism is used for converting rotary motion into areciprocating motion.


43/43

Oldhams coupling

An oldham's coupling is used for connecting two parallelshafts whose axes are at a small distance apart.

unit-i - kom slides.pdf

Documents