# MACHINE DYNAMICS CASE STUDY

Goal: To do a thorough kinematic analysis, compute the dynamic reaction forces in a linking mechanism, and clearly report the case study’s findings.

A frictionless slider linkage mechanism is shown in the above image. It consists of two homogeneous rigid rods, designated as OA and AB. Rocker OA is under torque T at the instant depicted and has constant clockwise angular velocity OA. The slider has mass B m, and the rods OA m and AB m each have a mass of one meter. In all computations, the weight of all rigid bodies can be disregarded.
A thorough kinematic analysis of the mechanism is required before designing it. In order to prevent mechanical failure, it is also necessary to analyze the reaction forces that are operating within the joints.

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Perform the following tasks at the instant depicted in the image using the individually assigned values of lengths OA, AB, h, angle 1??, angular velocity OA??, and masses OA m, AB m, and B m, which may be found in

OA (m) AB (m) h (m)? 1 (deg)? OA (rad/s) mOA (kg) m AB (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 of 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
[20]

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 centers for OA
(5) Acceleration of mass center for AB
[30]

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 centers.
(2) Using the Dalemberts Principle (or otherwise), calculate the instantaneous torque T required.
to drive the mechanism at the instant shown.
[30]

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.