This section consists of the torque calculations for motor and gearing requirements.  The initial calculations were determined using revised weights and measurements from the 1999-2000 teams design.  These calculations were then updated as the design progressed and changed.  The calculations take into consideration the length, center of gravity, and weight for each part of the arm.  These calculations are somewhat approximated but accurate enough for motor and gear selection.

 Weights (lbs) Lengths (in) A 15.0 a 5 B 4.00 b 25.5 C 3.00 c 33.0 x 15.50 y 14.56 Weights (lbs) Lengths (in) B 4.00 b-x 10.0 C 3.00 c-x 17.5 Shoulder Motor 494.0 lb-in Elbow Motor 214.0 lb-in Application Factor = 1.5 Load = 3.3 lbs

Necessary Dimensions:

1st Stage

 Gear Material # of Teeth Diameter (mm) Sun Metal 18 14 Planet (3) Metal 15 12 Ring Metal 48 34

2nd Stage

 Gear Material # of Teeth Diameter (mm) Sun Metal 21 16 Planet (3) Plastic 12 10 Ring Plastic 45 34

3rd Stage

 Gear Material # of Teeth Diameter (mm) Sun Metal 12 10 Planet (3) Metal 18 15 Ring Metal 48 34

Important Equations:

1.

where:

2.

where:

3.

1st Stage Calculations:

From motor literature operational speed of motor: 10702rpm

(since ring = 0)

2nd Stage Calculations:

arm becomes sun2 in the next set of calculations

3rd Stage Calculations:

arm2 becomes sun3 in the next set of calculations

Gear Ratio:

 57.6 : 1

Power loss in Gear Train of Firestorm 18V drill:

Input power from motor:

where:

T = Motor torque in Nm

n =  Motor speed in RPM

The resultant force between the sun and planet gears, Fs, can be calculated at each mesh assuming 2% losses per mesh.  A free body diagram of the gear train is displayed in Figure B.2.  From static analysis of this diagram the relationship between the force Fs and the force transferred to the arm, Fa.  The relationships for Fs and Fa are as follows:

where:

Ts = Torque in the sun gear

Figure B.2 – Planetary Gear Train Free Body Diagram

We calculate that 1.24Nm is transferred to the 2nd sun gear, 3.63Nm is transferred to the 3rd sun gear, and that the output torque is 13.5Nm.  Since the output speed is 185.74 rpm, the power at the exit of the gearbox is 263 Watts.