User:HowardJan/sandbox

Example 1
Example: A triangle has 3 points. Point O at the origin (0,0), point A (3,3) and point B (5,0). Using vectors AO and BO, calculate the area of the triangle. the area of the triangle is 7.5

An example for Jocobian Matrix
A robotic arm with link lengths l1 = 5 $$in.$$, l2 = 3 $$in.$$, l3 = 1.5 $$in.$$, initial angles theta1 = 30 degrees, theta2 = 45 degrees, theta3 = 15 degrees and angular velocities theta1dot = 15 degrees/s, theta2dot = 10 degrees/s, theta3dot = 5 degrees/s is feeding someone sitting at a table. Calculate the velocity of the utensil to ensure it is not dangerous to the person. Output: X: l1*cos(theta1) + l2*cos(theta1 + theta2) + l3*cos(theta1 + theta2 + theta3)], [l1*sin(theta1) + l2*sin(theta1 + theta2) + l3*sin(theta1 + theta2 + theta3)], [0], [1 J: -l1*sin(theta1) - l2*sin(theta1 + theta2) - l3*sin(theta1 + theta2 + theta3) -l2*sin(theta1 + theta2) - l3*sin(theta1 + theta2 + theta3)  -l3*sin(theta1 + theta2 + theta3)] [l1*cos(theta1) + l2*cos(theta1 + theta2) + l3*cos(theta1 + theta2 + theta3)  l2*cos(theta1 + theta2) + l3*cos(theta1 + theta2 + theta3)  l3*cos(theta1 + theta2 + theta3)

f0_v_4: -1.16025604946161], [1.26914193776358