Kinematics of Machinery

Rotary to
Linear.

Analyze the relationship between crank angle and slider displacement. Determine velocity and acceleration profiles in reciprocating mechanisms.

1.0 Objective

To determine the linear velocity of the slider through theory and experiment when the angular velocity of the crank is set to 2.0 rad/s.

2.0 Introduction

In this laboratory, we investigate the kinematics of a simple mechanism used to convert rotary motion into oscillating linear motion and vice-versa. The bench-top unit demonstrates conversion of smooth rotary motion into reciprocating motion. The input angle is set on the crank plate and the slider displacement is read from the measuring scale.

The crank radius can be adjusted to different positions. A simple bolt insertion enables the swiveling cylinder to be locked, allowing demonstration of crank drive behavior.

3.0 Apparatus

Crank and connecting rod apparatus.

θ r L Slider

Figure 1: Simple crank and connecting rod sketch

4.0 Kinematic analysis

There are three types of planar rigid body motion:

Translation

Translation occurs if every line segment on the body remains parallel to its original direction during the motion. When all points move along straight lines, the motion is rectilinear translation. When curved, the motion is curvilinear translation.

Rotation about a fixed axis

All particles of the body, except those on the axis of rotation, move along circular paths in planes perpendicular to the axis of rotation.

General plane motion

The body undergoes both translation and rotation. Translation occurs within a plane and rotation occurs about an axis perpendicular to this plane.

Slider-crank relationships

Geometry

r = 25.0 mm, 37.5 mm, 50.0 mm  •  L = 150.0 mm

Displacement (theoretical)

x = r cosθ + √(L² − r² sin²θ)

Velocity (theoretical)

ẋ = r x sinθ · ωr cosθ − x

Velocity (experimental)

ẋ = dx · ω

Take ω = 2.0 rad/s

5.0 Procedure

1. Set the crank radius ($r$) to the specified length.

2. Attach the connecting rod ($l$) to the slider.

3. Rotate the crank to 0° (Top Dead Center) and zero the gauge.

4. Rotate crank in 30° increments and record slider displacement ($x$).

5. Repeat for full 360° revolution.

6. Plot Displacement vs. Angle curve.

6.0 Result

Complete tables, plot x vs θ, determine dx/dθ, and compare

Angular velocity

ω = 2.0 rad/s

Enter experimental x in cm in Table 2. The page will compute dx/dθ, experimental velocity, and percentage error.

Table 1: Theoretical value

θ (°) x (cm) ẋ (cm/s)

Table 2: Experimental data

θ (°) x (cm) dx/dθ (cm/rad) ẋ (cm/s)

Table 3: Percentage error (velocity)

θ (°) % error

Plot: x (cm) vs θ (deg)

7.0 Discussion

  • i) Explain how a crank and slider system works.
  • ii) Compare and discuss the result from the theoretical and experimental tables.
  • iii) Give your comment or suggest any cause of errors.
  • iv) Explain some practical applications of a crank and slider mechanism.

8.0 Conclusion

Write your conclusion about the experiment.

9.0 References

List all the references that you have made during the course of your findings.

"Mechanism Architect" Challenge

🛡️

Vault signature missing

Angle (θ)

Disp (x)

0.0mm

Bonus: Dead center challenge

Stop exactly at TDC (0°) or BDC (180°) while spinning.

Score

0 pts

Real-World Applications

Where Do You See It?

Slider-crank mechanisms quietly power many everyday machines: from car engines and refrigeration compressors to hand-operated pumps and punching presses.

  • Car engines: crankshaft converts piston motion into wheel torque.
  • Compressors: pistons draw in and compress air or refrigerant.
  • Hand pumps & jacks: your hand motion becomes lifting force.

Mini Game

"Everyday Machine Match"

Read the scenario and tap the device that MOST likely uses a slider-crank mechanism.

Quiz Score: 0/0

Assessment Matrix

Laboratory Item Score 5 (9-10) Score 4 (7-8) Score 3 (5-6) Score 2 (3-4) Score 1 (0-2)
1. Org & AppearancePerfect sequence. Diagrams intact. Slips correct. Cover bound. Single PDF.Format good. tidy. 1 detail missing. tape ring bound.Rough format organization uneven multiple language mistake stapled.Sloppy damaged inserts torn slips whiteout staples poorly.Absent.
2. Objectives & TheoryRephrased clearly own sentences. linking course research included beyond manual.Objectives identified sharp manual paraphrase.Objective partial definition manual copy.Verbatim manual minimal research objectives missing.Absent.
3. ApparatusList machine labeled diagram own words safety photo included report attached.Vital items minor omission manual paraphrase.partial list omissions key missing difficult steps.Equipment missing confused unnumbered manual copy.Absent.
4. Results (x2)Accurate organised trends clearly Easy figureNumbered walkers captions walkthrough.Correct trends drawn obvious minor figure problems units.missing data sloppy inaccuracy incomplete tables.Figures bad numbers construct poor construction.Absent.
5. Discussion (x2)Ans allaccurately links trends outcomes theory objectives analyzed error reduce.miss one answer correctly results interpret gap.Incomplete understanding partial evident inconsistencies.Lack understand indicator indicators comparison.Absent.
6. ConclusionSummary summaries data achieved valid validity suggests improvement.Missing condition excellent excellenty met.Missing excellently element missing met.missing excellente conditions excellently.Absent.
7. ReferencesMultiple source journal book manual 30% references < 5 years.6 - 8 source written manual observed.3 - 5 format comply partial compliance.1 - 2 cited ignore formatting reference standard.No references.

Performance log

Complete Section 6.0 tables and write-ups (7.0–9.0), then preview/export your PDF submission here. Game + quiz marks are included automatically.

Marks summary

Games

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Quiz

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Export report

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