Question: matlab question computer science mathematical computing in the engineering...
Question details
MATLAB QUESTION
(COMPUTER SCIENCE / MATHEMATICAL COMPUTING)
In the engineering industry, a fourbar linkage is often used in pumpjacks, footoperated machines i.e. lathe machines, gear shift linkages and steam engines and locomotives. The mechanism consists of four links connected in a loop by four joints. A diagram of the mechanism is shown below. The first link, π, is the input link (crank). The second link, π, is a coupler link. The third link, π is the output link. The fourth link, π, is the fixed link (ground).
The angular position of the output link (π4) of a fourbar linkage corresponding to the angular position
of the input link (π2) can be computed using the Freudensteinβs equation:
The length of the links are as follow: π = 1 unit, π = 2 units,
π = 4 units, and π = 5 units. The following parameters can be used
for root finding:
π₯π = 120Β°, π₯πβ1 = 110Β°, πΏ = 0.01, ππππππ πππ = 0.001
PART A
Find the value of π½_{π} for π½_{π} = ππΒ° using
any open root finding method.
Subsequently, create a stick figure image of the fourbar linkage
when π2 = 60Β° with the following specifications:

 Link π

 Link π

 Link π
Line specification: Blue solid line with thickness of 8. Line specification: Green solid line with thickness of 8. Line specification: Red solid line with thickness of 8.
Axes ranges should be set to the same axes ranges shown in the picture below. Ensure that the grid is turned on.
PART B
Find the values of π_{4} for π_{2} = 0: 1: 360Β° using any open root finding method of your choice. You can monitor the outputs of all iterations to help you choose a suitable root finding method. In a new figure, plot a graph of output angle versus input angle using red asterisks.
PART C
Animate the stick figure created in Part A In a new figure window, use the calculated values of π4 from Q1b to show an animation of one complete revolution (for π2 = 0 to 360Β°). Ensure that all links are moving in a logical manner where the length of π, π and π are constant and cannot be changed. Axes ranges should be set to the same axes ranges in Q1a. Ensure that the grid is turned on. The current π½_{π} value should be stated in the title.
The following MATLAB functions: plot() and pause() will need to be used.
To achieve an animation effect, the coordinates of links quickly
will need to be updated quickly. A pause of 0.01 seconds is
recommended.
The stick figure animation should look like the following (at the
respective instances):