Robotic Arms, Mathematics Problems

November 22, 2014

Example Problem:
A small servo weighs 9g and has a maximum torque of 1500g/cm. We want to know what the biggest weight that can be lifted by the arm that we have. Where: L1 = 10cm; L2 = 8cm; L3 = 11cm; W1 = 35g; W2 = 9g; W3 = 30g
The forces acting at M1 are going to be greater than those of M2 so we can solve our M1 equation for W4 and get our answer.
M1 = L1/2*W1 + L1*W2 + (L1+L2/2)*W3 + (L1+L3)*W4
W4 = (M1 - L1/2*W1 - L1*W2 - (L1+L2/2)*W3)/(L1+L3)
W4 = 38.8g

The math says that the robot arm can lift 39g; but the arm probably cannot lift 39g in the real world due to friction and the mechanics of the servo motor. All that considered we are still lifting a 39g load at a 21cm distance with a motor that only weighs 9 grams. To gain better performance the servo should be a stronger servo; or the design of the arm needs to be changed by making it shorter or making it weigh less.