How can i analysis this system?

The figure shows a mechanism designed to transfer load from one conveyor line (k1) to the other (k2). The O2A arm, which makes a full revolution, causes the BO4C pendulum to oscillate, and this movement is transferred to the D limb, which pushes the load through the connecting rod CD, enabling the load to be transferred from k1 to k2 and then to the D limb coming back again. When the BO4C arm is considered as a triangle, the angle of the BO4C arm is 15 degrees.

a) Let the angle made by the O2A arm with X be theta_2. Write a program in Matlab that performs position analysis for its rotation at 1-degree intervals between 0 and 360 degrees. Show how the mechanism works (animated) with the help of this program.

b) Calculate the movement of point D in the horizontal direction and draw the graph of its change with the angle theta_2 (horizontal axis theta_2 degrees) and calculate the stroke of point D.

c) Draw the graph of the change in the angles of the limbs with theta_2 angle (all in the same graph, the horizontal axis will be in theta_2 degrees and the vertical axis will be in degrees).

d) The going and returning movement directions of point D are shown in the figure. If the arm O2A rotates in the direction  with constant angular speed, calculate the ratio t_go/t_return.

e) Recalculate the lengths of the drive pairs O2A and AB so that the round trip time ratio of point D is t_roundtrip/t_turn=1. In the new situation, will the location of the O2 point change? Where will it be compared to its initial position?

f) Re-animate the mechanism and show whether the round trip time ratio is really 1.

g) Recalculate the requirements in (a-c) above.

h) Let the angular speed of the O2A arm be a constant 15 rpm in the counterclockwise direction. In this case, draw graphs of the change in the speed and acceleration of point D with the angle theta_2 (horizontal axis theta_2 degrees).

i) Calculate the angular speed (rad/s) and acceleration (rad/s^2) of the limbs and draw graphs of their changes with theta_2 angle.

[the cyclist]

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Answer 1

[Sulaymon Eshkabilov]

Oksan,

(1) Derive kinematic equations (relationships) of the bars and components: O2A vs. other bars

(2) Write a code

• Start your code by intializing an input variable (angular displacement O2A): a = 0:360
• Put the expressions in a sequantial order from part 1 to perform calcs
• Plot the results: animate

... here is a nice code on how to start animation coding for a slider mechanism: https://www.mathworks.com/matlabcentral/fileexchange/67495-slider_animate