create a fourbar mechanism calculator in matlab

To create a fourbar mechanism calculator in Matlab, we can define a function that calculates the position and velocity of the end effector of the mechanism based on the configuration of the links. We can use the following steps:

  1. Define the lengths of the four links.
L1 = 4; % Length of link 1
L2 = 3; % Length of link 2
L3 = 5; % Length of link 3
L4 = 2; % Length of link 4
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  1. Define the initial configuration of the mechanism.
theta1 = 0;   % Angle of link 1
theta2 = pi/6; % Angle of link 2
theta3 = pi/3; % Angle of link 3
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  1. Define the position of the fixed pivot point.
P1 = [0 0]; % Position of pivot 1
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  1. Calculate the position of the moving pivot point.
P2 = P1 + [L1*cos(theta1) L1*sin(theta1)]; % Position of pivot 2
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  1. Calculate the position of the coupler point.
P3 = P2 + [L2*cos(theta2) L2*sin(theta2)]; % Position of coupler point
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  1. Calculate the angle of the line connecting pivot 3 and the end effector.
alpha = acos((L3^2 + L4^2 - norm(P3)^2)/(2*L3*L4)); % Angle of line connecting pivot 3 and end effector
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  1. Calculate the position of the end effector.
P4 = P3 + L3*[cos(theta3+alpha) sin(theta3+alpha)]; % Position of end effector
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  1. Calculate the velocity of the end effector.
V4 = [-L3*sin(theta3+alpha)*theta3_dot-L4*sin(alpha)*(theta2_dot+theta3_dot); L3*cos(theta3+alpha)*theta3_dot+L4*cos(alpha)*(theta2_dot+theta3_dot)]; % Velocity of end effector
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We can then define a function that takes the angles and their derivatives as inputs, and outputs the position and velocity of the end effector.

function [P4,V4] = fourbar_mechanism(theta1,theta2,theta3,theta1_dot,theta2_dot,theta3_dot)

L1 = 4; % Length of link 1
L2 = 3; % Length of link 2
L3 = 5; % Length of link 3
L4 = 2; % Length of link 4

P1 = [0 0]; % Position of pivot 1
P2 = P1 + [L1*cos(theta1) L1*sin(theta1)]; % Position of pivot 2
P3 = P2 + [L2*cos(theta2) L2*sin(theta2)]; % Position of coupler point

alpha = acos((L3^2 + L4^2 - norm(P3)^2)/(2*L3*L4)); % Angle of line connecting pivot 3 and end effector

P4 = P3 + L3*[cos(theta3+alpha) sin(theta3+alpha)]; % Position of end effector
V4 = [-L3*sin(theta3+alpha)*theta3_dot-L4*sin(alpha)*(theta2_dot+theta3_dot); L3*cos(theta3+alpha)*theta3_dot+L4*cos(alpha)*(theta2_dot+theta3_dot)]; % Velocity of end effector
end
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