Robot Arm Design: Calculating Torque Needed

[jmay]

I am design a three jointed robotic arm that can lift 40 pounds. A diagram of the arm is attached.
How can I calculate the torque needed at each motor to lift the 40 pounds?

 

[schip666!]

torque = distance times mass = e.g. Foot-Pounds

is that what you need?

 

[jmay]

That's how I've been doing the calculation. This finds the torque at the full extension of the arm. How can I find the torque need at half extension? Would I find the lifting angle and multiply by the sin of the angle?