intro to mechanisms

8/18/2019 Intro to Mechanisms

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ME316: Kinematics and Dynamics

of Machines

Abhishek Gupta

IIT Bombay



Mechanisms



Function generation mechanisms

Input – output link motions are related



Motion generation mechanisms

Motion of a link is controlled



Developed by James Watt Approximate straight line

mechanism

Used to prevent lateral

movement of real axle

Motion of a reference

point is of concern

Watt’s linkage



Degrees of freedom (DOF)

DOF: Number of independent parameters required touniquely define the position of a system at any instant of

time

A mechanical systems mobility can be classified according

to the number of degrees of freedom Types of motion

Pure translation: All points on the body describe parallel

(curvilinear or straight) paths

Pure rotation: One point on the body (center of rotation) hasno motion with respect to the fixed frame of reference. All

other points move in circular arcs.

Complex motion: Simultaneous translation and rotation



Links and joints

A link is a rigid body that posses at least two nodes Nodes are points of attachment of other links

Binary link: 2 nodes

Tertiary link: 3 nodes

Quaternary link: 4 nodes A joint (or kinematic pair) is a connection between two

or more links (at their nodes) that allows motion



Classification of joints

Joints can be classified base upon The type of contact between the links

Lower pair – surface contact

Higher pair – point or line contact

Number of degrees of freedom allowed at the joint By the type of physical closure

Form closed – links are kept together by geometry

Force closed – require external force to keep links together

By number of links joined

Order of a joint is one less than the number of links joints



Kinematic pairs

Kinematic pairs describe the relative motion betweentwo bodies

Lower pairs – joints with surface contact



Higher kinematic pairs

Higher pairs – joints with point or line contact



Some definitions

Kinematic chain: Links joined together to provide acontrolled output motion to a supplied input motion

Mechanism: A kinematic chain in which at least one link is

“grounded” (attached to the frame of reference)

Machine: Mechanism designed to do work Link classification

Ground: Link or links that are fixed with respect to the

reference frame

Crank: Pivoted to ground. Makes complete revolution

Rocker: Pivoted to ground, has oscillatory motion

Coupler: Not attached to ground, has complex motion



Drawing kinematic diagrams



Determining degrees of freedom

Gruebler’s equation for planar mechanisms

DOF = 3(N-1) – 2L - H

DOF : Degrees of freedomN : number of links

L : number of lower pairs

H : number of higher pairs



Drawing kinematic diagrams

Slider-crank mechanism

Weight-training machine



Example - DOF



Example – DOF: multiple joints

Multiple joints count as one less than number of links joined at the joint



Example – DOF: Higher pair

Higher pair allows motion in 2 DOF

Link 3 can roll and slide



Mechanisms and structures

If DOF > 0, the assembly of links is a mechanism and will exhibit relative motion

If DOF = 0, the assembly of links is a structure and will exhibit no motion

If DOF < 0, then the assembly is a preloaded structure, no motion is possibleand stresses are present



Example – Limitation of gruebler’s equation

Find the degrees of freedom of these mechanisms

Using Gruebler’s equation

By inspection

Gruebler criterion does not include geometry!

We must use inspection to verify the prediction



Rolling cylinders

Number of links: 3 If no slip is allowed

Number of joints that allow singleDOF: 3

Gruebler’s equationDOF = 3(3-1) – 2*3

= 0

But we know that the mechanismhas 1 DOF

Length of ground link is exactly the sum of other two links



DOF in spatial mechanisms

DOF = 6(N-1) – 5J1 – 4J2 – 3J3 – 2J4 – J5

N: number of links

Jn: joint with n degrees of freedom

Example - Stewart platform



Kinematic inversion

Method of obtaining different mechanisms by fixingdifferent links of a kinematic chain

Relative motion of links is not changed

Absolute motions with respect to the fixed link may change



Grashof’s law

If the link lengths for a four bar mechanism be s (shortestlink), l (longest link), p and q and

l + s ≤ p + q

then the shortest link can rotate fully with respect to the

neighboring link

If l + s > p + q

then only double-rocker mechanisms are possible

How is link length measured?



Inversions of the four bar mechanism

l + s ≤ p + q One double crank (drag-link)

Shortest link is ground

Two different crank rocker mechanisms

Shortest link is crank

One of the adjacent links is ground

One double-rocker

Shortest link is the coupler



Change – point condition

If l + s = p + q

Eg. Parallelogram mechanism

Follower may change directionat the critical location



Examples

Beam engine – crank rocker

Coupling rod – double crank

Watt’s linkage – double rocker



Inversions of a single slider crank

Oscillating cylinder engineSingle slider crank

Pendulum pump Rotary internal combustion engine



Inversions of a double slider crank

Scotch yoke mechanismA mechanism to draw an ellipse

Oldham’s coupling



Whitworth Quick-Return Mechanism

intro to mechanisms

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