A mechanism known as a four-bar linkage is shown in the figure below.

Mechanisms such as this are used in mechanical systems to generate a specific output motion in

response to an input motion. This four-bar linkage is a one-degree-of-freedom mechanism; if the

position of any one of the links is known, the position of all of the other links can be found.

Assume that there is a motor driving link 2; if the angle of link 2 (2) is specified, the angle of

link 4 (4) can be found through the solution of the following equation:

l1 = l4 cos4 l2 cos2 + l3

2 (l4 sin4 l2 sin2 )2

where li is the length of link i. (Note that link 1 is an implied link, and simply specifies the

distance between the two rotational pivot points.)

Write a Matlab program that uses root finding to find the input angles (2) that would produce an

output angle 4 = 80, for the mechanism above with l1 = 6 in, l2 = 4 in, l3 = 7 in, and l4 = 5.2 in.

For full credit, your program should not use the

fzero (or any other) built-in Matlab root finding

functions. Instead it should call a function you write yourself that uses the bisection method

discussed in class to find a root. Your function should be able to estimate and return a root of

any function, given the brackets containing a root, the function handle, and a tolerance passed to

it as input arguments. (Note that getting your main program working at first by calling the fzero

function and testing your root finding function by comparing the results to the fzero function are

very good ideas.) If you cannot get your function working correctly, call the fzero function in

your program instead of your own function, for partial credit.

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