Structural Issues in Linkages

8/22/2019 Structural Issues in Linkages

1/22

6/14/2013Me 3230Page 1

Structural Issues in Linkages

R. Lindeke, Ph. D.

ME 3230 Kinematic &Mechatronics


2/22

6/14/2013Me 3230Page 2

Topics Of Interest

Grashofs Law

Motion Limits for Slider Cranks

Interference in Linkages

Mechanical Advantage

Practical Considerations

Revolute Joints

Prismatic Joints


3/22

6/14/2013Me 3230Page 3

Grashof Law

The fundamental 4-bar linkage design law:s + l < p + q

Here, s is the shortest link l is the longest link

p and q are the other two links

This law states that for there to be

continuous relative motion between any 2links, this inequality must be true (GrashofType 1 linkages)


4/22

6/14/2013Me 3230Page 4

Consequences of Failure ofGrashofs inequality:

Links cant connect!s+l+pq

Links cant connect!s+q+p


5/22

6/14/2013Me 3230Page 5

Type 1 or 2 Grashof Linkages

Type 1: the inequality holds

We state that these linkages (type 1) have

two joints that perform complete (360)rotation and they are located at eitherend of the shortest link

Type 2: the inequality is not held

They have no fully rotating joints

All 4 joints oscillate between limits


6/22

6/14/2013Me 3230Page 6

Addition Type 1 Nomenclature

Base frame is the fixed link

Two members connected to base by

revolute joints are Turning Links Member jointed to both turning links is

the Coupler


7/22

6/14/2013Me 3230Page 7

Type 1 Mechanisms:

s is connected to thebase (a, b) this is acrank rocker

s is the base link (c)this is double crank ordrag-line mechanism

s is the coupler linkthis is a double rockerwhere the coupler can

perform a completerotation relative to thebase


8/22

6/14/2013Me 3230Page 8

Topological Interference So itshould rotate shouldnt it?

This point is really one of construction making surethat the design will actually operate

Topological interference is a fundamental property of

the structureit cant be eliminated by reshapinglinks

When we are assembling a Linkagethere is a rightway to assure that the various links will not runthrough each other

Motion will be transferred to rotating link usingshafts (perhaps) so this issue also addresses how theshafts are connected to the linkage too


9/22

6/14/2013Me 3230Page 9

A Simple Crank rocker as astructure

Notice the Positioning of Coupler vs. the turninglinks (a). In this arrangement we can bringin/take out torques with shafts thru the base link(b). And the crank can completely rotate withoutstriking the shaft or coupler!


10/22

6/14/2013Me 3230Page 10

Setup for Drag Link Mechanisms

Here the drive Shaftsmust be connected directlyto the turning links

In the drag line, the baselink has become a pair offixed bearings and the linkis essentially turned insideout

This is a must otherwisethe coupler must pass thruthe base or shafts thusbecoming locked up


11/22

6/14/2013Me 3230Page 11

Lets try one:

Problem 1.35 where you are to selectfrom a set of 8 links (2; 3; 4; 7;

9.5; 13 and 9) From this set choose4 links to build a mechanism that canbe driven by a continuous rotational

motor? Identify each link byappropriate name.

What type of mechanism results?


12/22

6/14/2013Me 3230Page 12

Motion Limits for a Slider Crank

There are 2 rules thatmust be held forfreedom of motion fullrotation

b>a in mechanism b - a > c

Where a is length ofcrank

Where b is length of

coupler Where c is the distance

from ground pivot toslider pin


13/22

6/14/2013Me 3230Page 13

Design Considerations

Consider Slider Crank Half first A-B-C: does it meet motion criteria? BC>AB (yes) BC-AB>c (yes)

Consider C-BD-EF-AF as a crank

rocker EF must be the crank we will let

upper link (A-B-D) rock to movethe Slider at C

Positioning of E is along the locusof E (from DE length) -- upper

sketch Use Grashof calculation for the

shortest link of Crank-rocker toestablish true limits for E (lowersketch)


14/22

6/14/2013Me 3230Page 14

Mechanical Advantage in a Mechanism

MA is the ration of the outputtorque to the input torque of amechanism

This ration is directly proportionalto Sin() (coupler to driven turner)and inversely proportional to Sin()

(coupler to driver turner) When is 0 or 180 (position A-B1

and A-B2 in the figure) a smallinput torque delivers a large(infinite) output torque the rockeris said to be in Toggle

When is small MA is very lowthis transmission angle shouldnever be designed to work atangles of less than about 45 . IfMA is too small, only a smallamount of friction can lock up themechanism


15/22

6/14/2013Me 3230Page 15

Mechanical Advantage in a Mechanism

Considering rin & rout as level arms of theinput and output shafts (and loads), then:

4

2

. .( )

is angle from driven link (4) to Coupleris (smallest) angle from driver link (2)

to Coupler

in

out

Link SinrM A

r Link Sin


16/22

6/14/2013Me 3230Page 16

Try One?

A crank-rocker linkage has a 100-mmframe, a 25-mm crank, a 90-mm

coupler, and a 75-mm rocker. Draw thelinkage and find the maximum andminimum values of the transmission

angle. Locate both toggle positions andrecord the corresponding crank anglesand transmission angles.


17/22

6/14/2013Me 3230Page 17

Green Lines AtGamma limits Crank at 0 or 180

is about 53.1 and98.1 respectively

Purple Lines at Toggle

Crank at about 226 and40 (rocker back andforward respectively)

is about 90.9 and59.1 respectively


18/22

6/14/2013Me 3230Page 18

Practical Design Issues: RevoluteJoints

Lubrication of the Bearing Surfaces in rotation Hydrodynamic lubrication occurs under conditions

of unidirectional rotation under speed

A lubricating film, carrying the bearing load, isestablished between the bearing surfaces and onlylubricant viscous friction (low friction) results

additionally no metal to metal contact is present and norunning wear is observed (only startup and stoppingwear)

Lubricant can by pumped in to assist in establishing HDlubrication

HD lubrication is seen in internal combustion engines forcrankshaft support bearings and connectingrod/crankshaft bearings


19/22

6/14/2013Me 3230Page 19


Lubrication of the Bearing Surfaces in rotation

Hydrostatic lubrication is a system where lubricantis pumped in to the bearing gap under elevatedpressure to carry the bearing loads

It can be used even if rotational speed is low or evenreverses

Used in main bearings in large turbo-generator sets

Fits need to be made to tight tolerances so oil will notleak out in operation or idle activities


20/22

6/14/2013Me 3230Page 20


Can use Grease Bearings in slow orreversing motion

Solid Contact bearing (teflon bearings) and

dissimilar metal bearing can be used likebabbitts metal 90% tin 10% copper 89% tin 7% antimony 4% copper 80% lead 15% antimony 5% tin

Also can use roller, ball or pin bearings ascontactor for revolute joint systems


21/22

6/14/2013Me 3230Page 21

Practical Design Issues: PrismaticJoints

Jamming of the slider is purely a design issue!

This problem is a function of the friction of the slider, theapplied force and its direction If the angle of the coupler to slider is less than the Friction angle:

f = tan-1m (mis coefficient of friction) the slider will jam Sliders loaded by offset forcing loads will also Jam if the width

of the slider b < 2 mawhere a is the offset between the sliderand the forcing load


22/22

6/14/2013Me 3230Page 22

Practical Design Issues: PrismaticJoints

Since Jamming is a function of slider friction, usingmeans to reduce friction is the most effective way toreduce problems

The use of rolling contact joints is an effect means toreduce the friction

Documents

Structural Issues in Linkages