Torque

In order to compute the torque needed to pick up a 200g body, we know that we have three screws allowing us to move in the three coordinates frames, perhaps we are using a steel rod as a guide in the X axis to assure the correct displacement.

We are developing the calculations for the screw in the x axis, because this is the one who is supporting a larger weight. (It supports the Y and Z axis)

From the book “Shigley´s Mechanical engineering design” in chapter 8 “Screws, fasteners, and the design of Nonpermanent joints”, we get the formula allowing us to compute the torque needed by the screw to move the weight to which it is subjected.

Where,

Tr = Torque.

F = Force on the screw.

dm = Pitch diameter.

f = Friction .

l = Lap advance.

The pitch diameter is computed by the next equation:

The lap advance is the same as the pitch of the screw, which means 4mm by revolution.

The friction coefficient is gotten from table 8-5 in the same book, the value is 0.17 since we have a brass flange.

To get the force on the screw we add the weights of the structure supporting the x axis (2 aluminum profiles and 4 guides), and the weight of the body to pick up.

The weight of the aluminum profiles is 0.9 kg/m, we have two profiles of .24 each, then a total weight of 0.432 kg. Further, each guide has a weight of 2.44g, for a total of 9.76g. The gripper has a mass of 40g. For a total weight of 0.48176 kg.

Thus:

Calculating torque, we get:

Since the stepper motors we chose provide us with a torque of 0.4 Nm we can confirm that we are going to be able to pick up a 200g body.