laboratory on mechanisms

7/29/2019 Laboratory on Mechanisms

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The University of Western AustraliaSchool of Mechanical Engineering

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Mechanisms and Multibody Systems

MECH3422 (630.319)(Prof Karol Miller)

Laboratory Exercise

Analysis and Design of Planar Mechanismshttp://www.mech.uwa.edu.au/units/MECH3422

Demonstrator: Chris Jiajie Ma ([email protected])

Laboratory report submission: please ask lab demonstrator

Equipment required:Ruler, protractor, calculator, and graph paper.

A. Construction and Analysis of a Quick-Return Slider-Crank

Mechanism.

Introduction

In many applications, mechanisms are used to perform repetitive operations such as pushing partsalong an assembly line, clamping parts together while they are welded, or folding cardboard

boxes in an automatic packaging machine. In such applications it is often desirable to use a

constant speed motor. In these repetitive operations there is usually a part of cycle when the

mechanism is under load, called the advance or working stroke, and a part of the cycle, called the

return stroke, when the mechanism is not working but simply returning so that it may repeat the

operation. The linkage of Fig.A1b is called the general or offset slider-crank mechanism. Certain

special effects can be obtained by changing the offset distance e. For example the distance B 1B2

is always larger than twice the crank radius. Also the crank angle required to execute the forward

stroke is different from that for a backward stroke. This feature can be used to synthetise quick-

return mechanisms where a slower working stroke is desired.


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Fig.A1 a) On-centre slider-crank mechanism;

b) General (or offset) slider-crank mechanism.

For example, in the offset slider-crank mechanism (Fig.A2) work may be required to

overcome the load while slider moves to the right (from C1 to C2) but not during its return

to position C1 since the load is removed. In such situations, to keep the power

requirement of the motor to minimum and to avoid wasting valuable time, it is desirable

to design the mechanism so that the slider will move faster through the return stroke than

it does during the working stroke, i.e., to use higher fraction of the cycle time for doing

work than for returning.

Figure A2. Quick-return mechanism offset slider-crank mechanism.

A measure of the suitability of a mechanism from this viewpoint, called advance- to

return-time ratio is defined by the formula:

Q=(time of advance stroke)/ (time of return stroke) (1)


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Mechanisms with Q>1 are called quick-return mechanisms.

Assuming that the driving motor operates at constant speed, it is easy to find the time

ratio. The first thing is to determine the crank positions which mark the beginning and

end of the working stroke (points B1 and B2 in Fig. A2). Next we can measure the crankangle travelled through during the advance stroke and the remaining angle of thereturn stroke. The advance- to return-time ratio is then:

Q= / (2)

Notice that the time ratio of a quick-return mechanism does not depend on the amount of

work being done or speed of the motor. It is a purely kinematic property of the

mechanism itself and can be found strictly from the geometry of the device.

We also notice that there is proper and improper direction of rotation for such a device. If

the direction is reversed the roles of and would reverse and the time ratio would be

less than 1.

Laboratory work

Design and build a quick-return slider-crank mechanism (Fig. A1b) using the following

dimensions as guidelines:

r2=2 (or 4); r3=10 (in Lego horizontal units); e=8 (in Lego vertical units).These are only a guide! They dont have to be exact - if your design is easier to build and/or

operates more easily because youve changed the dimensions slightly, thats fine, but make sure

you document reasons for changes.

Ask a lab demonstrator for help to quickly build the mechanism, including pre-prepared

gearbox and angle encoders.

Report Part A

Measure the actual dimensions of your mechanism (lengths and angles). Includereasons for any changes made.

Calculate the stroke and time ration from the length measurements and trigonometry.

Compare these to the results from measured angles, and what was expected from theinitial design. Comment on differences or irregularities, and suggest possible reasons.


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B. Design of a crank-and-rocker mechanism

Introduction

Figure B1 shows a four-bar linkage called the crank-and-rocker mechanism. Crank 2

drives rocker 4 through coupler 3. The characteristics of the rocking motion depend on

the dimensions of the links and the placements of the frame points.

Figure B1. Four-bar linkage called the crank-and-rocker mechanism.

The limiting positions of the rocker in a crank-and-rocker mechanism are shown as points

B1 and B2 in Fig.B2. Note that the crank and coupler form a single straight line at each

extreme position. In this particular case the crank executes the angle while the rockermoves from B1 to B2 through the angle . Note, on the back stroke the rocker swings from

B2 back to B1 through the same angle but the crank moves through the angle 2 - .There are many cases in which a crank-and-rocker mechanism is superior to a cam-and-

follower system. Among the advantages over cam systems are smaller forces involved,

the elimination of retaining spring, and the closer clearances because of the use of

revolute pairs.

If> , then =, where can be obtained from the equation for the time ratio

Q=(+)/() (3)

of the forward and backward motions of the rocker.


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Figure B2. The extreme positions of the crank-and-rocker mechanism.

Laboratory work

1) Build a crank-and-rocker mechanism with characteristics as close as possible to the

following:

output angle =75 deg; time ratio Q=1.32; rocker length r4=6 [Lego horizontalunits].

The synthesis of this mechanism is achieved easily using a graphical method, Fig.B3, and

following the steps outlined over the page.

Figure B3. Synthesis of a four-bar linkage to generate the rocker angle .

a) Compute using eq.3


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b) Locate point O4 and draw the two positions O4 B1 and O4 B2 of link 4 separated by the

angle as given (Fig. B3a).c) Through B1 construct any line X.

d) Through B2 construct line Y at the angle to X. The intersection of these two linesdefines the location of the crank pivot O2. Since any line X was originally chosen, there

are an infinite number of solutions to this problem.e) The distance B2C is 2*r2, twice the crank length. The coupler length is r3= O2 B1 -r2.

Since there are an infinite number of solutions, if you arrive at one which is unrealistic or

difficult to build, refine it!

Ask a lab demonstrator for help to quickly build the mechanism, using gearboxes and

encoders prepared previously.

2) Operate the mechanism and measure input and output angles of the mechanism.

Report Part B Include a copy of your initial design sketch (labelled photocopy is fine)

Measure the actual mechanism dimensions (also measure angles if you have aprotractor).

Calculate angles and time ratio from length measurements and trigonometry showall working.

Comment on any differences between calculated and measured results, including possible

reasons for deviations.

Reports (4% of final mark for the unit, report is marked on the 1 to 10 scale: 1

point = 0.4%)

One report per group is required. High quality of submission is expected.

In addition to performing the exercises you are expected to submit a report describing

your results. The report should contain the following:

(a)A description of steps you performed(b)For each part, sketch the mechanism and include all calculations and plots as outlined

within sections A and B. Make sure all questions are answered and discuss results as

requested.

(c)Conclusions.

Your demonstrator, who will also be responsible for marking, will expect neatpresentation, and evidence that you have put some thought into your report. The report

should be submitted to your demonstrators assignment box within 2 weeks of doing the

lab.


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Reference:

J.E. Shigley, J.J. Uicker Jr, Theory of Machines and Mechanisms, McGraw-Hill, 1995.

Appendix: Lego units

laboratory on mechanisms

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