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MACHINE DYNAMICS CASE STUDY

Aim: To conduct a full kinematic analysis and calculate the dynamic reaction forces in a linkage

mechanism, and to present the results of the case study in a clear reporting format.

Introduction:

The above figure depicts a frictionless slider linkage mechanism, consisting of 2 homogenous rigid rods, OA and AB . At the instant shown, rocker OA is subjected to torque T and has constant clockwise angular velocity OA ??. The rods have masses OA m and AB m, and the slider has mass B m . The weight of all rigid bodies can be ignored in all calculations.

To design the mechanism, a careful kinematic analysis of the mechanism needs to be conducted. Moreover, the reaction forces acting within the joints need to be analysed to avoid mechanical failure.

Tasks:

At the instant shown in the figure, perform the following tasks using the individually assigned values of lengths OA, AB , h , angle 1 ??, angular velocity OA ??, and masses OA m , AB m , B m – these can be found in

OA (m) AB (m) h (m) ?1 (deg) ?OA (rad/s) mOA (kg) mAB (kg) mB (kg)

0.45 0.32 0.48 37 10 0.3 1.1 0.8

All calculations should be included in the report. Please use the notation defined in the above figure when reporting the results from your calculations.

A. Geometric Calculations:

Determine:

(1) Horizontal displacement z .

(2) Angle ?2.

B. Velocity Analysis:

Determine the magnitude and direction of:

(1) Velocity of point A .

(2) Angular velocity for rod AB .

(3) Velocity of point B .

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C. Acceleration Analysis:

Determine the magnitude and direction of:

(1) Acceleration of point A .

(2) Angular acceleration for rod AB .

(3) Acceleration of slider B .

(4) Acceleration of mass centre for OA.

(5) Acceleration of mass centre for AB

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D. Dynamic Analysis:

(1) Sketch a clear free-body diagram for each rod and the slider, taking care to show all forces

(including pin reaction forces) and accelerations for all mass centres.

(2) Using D’Alemberts Principle (or otherwise), calculate the instantaneous torque T required

to drive the mechanism at the instant shown.

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An additional 10 marks are available for well written reports. These marks will be awarded to students

who submit a concise report, containing the requested information with a clear presentation of numerical

results and diagrams. Lengthy reports that contain large amounts of repetition, trivial results and/or poor diagrams are unlikely to attract any of these marks.