After I read the robot arm tutorial, I asked myself: “what could prevent the vertical arm from leaning?” (the attached picture can clarify my point). I looked at the robot arm calculator but I didn't find anything mentioned about that. I did some math and I want to review it with you:
TL = (W0 * Sin (theta) * L0/2) + (W1 * Sin (theta) * L0) + (W2 * Sin (theta) * L0) + (W3 * Sin (theta) * L0) + (W1 * Cos (theta) * L1/2) + (W2 * Cos (theta) *(L1 + L2/2)) + (W3 * Cos (theta) * (L1+L2+L3/2))
= (W0/2 + W1 + W2 + W3) * L0 * Sin (theta) + (W1 * Cos (theta) * L1/2) + (W2 * Cos (theta) *(L1 + L2/2)) + (W3 * Cos (theta) * (L1+L2))
I neglected the weight of motors in order not to make the equation complicated, but I’m going to consider them later in my equation
TL: Torque around the fixed point.
W0, W1, W2, W3: The weights of the vertical, first, second linkage and load.
L0, L1, L2: The lengths of vertical, first and second linkage
Theta: leaning angle.
Do I miss something?
Now I want to get the optimum lengths of linkages that do not make the arm lean, if I’m given the weights and theta is 1 or 2 degrees, how can I continue?
If you can't see the image, please follow the link:http://img301.imageshack.us/my.php?image=armleanyn5.jpg