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Case study - motors and gears

In FIRST Steamworks the 2017 game involved the robots climbing a rope 4 feet into the air.  Hoya Robotics Team 4152 used two climbing mechanisms that year so it is a perfect case study for gear and motor combinations.
FYI - this page is being worked on.
 

Trillium The Robot

Trillium was 100lb robot with a 14lb battery and 20lb bumpers for a total mass of 134lb (595.64 Newtons).  This was calculated using:
F = mg 
where F is the force of gravity, m is the mass of the object in kg and g is equal to 9.8 m/s^2 on the surface of the Earth).
The challenge was to climb 4ft (1.22 Metres) of rope during the last 30 seconds of the match.  Ideally we want to ensure the rope climbing is 15 seconds or less - this gives us time to move the rope into position and catch the rope.

Climbing Mechanism #1:

Climber
The climbing mechanism was a shaft 2" (5.08cm) in diameter powered by a bag motor with a 256:1 gear reduction.
Bag motor curve

Bag Motor Specifications

 Free speed (RPM) 1400  The maximum speed at which a motor will rotate when under no load
 Free Current (A)   1.8 The minimum current a motor will draw when under no load
 Stall Torque (N ∙ m)  0.4 The amount of load placed on a motor that will cause it to stall (stop moving)
Stall Current (A)  41 The amount of current drawn by a motor when it is stalled

Formulas

Electrical:
P = I*V
P - Power in Watts
I - current in amperes (or amps)
V - electric potential in Volts

Mechanical:
Torque = Force * Distance or Force = Torque/Distance

Work = force x Distance

Power = Work/Time

Calculations

Our robot uses a 12 Volt battery and the fuse for the motor circuit is rated at 40 amps - we want to ensure we are only using 35 amps to not risk tripping the fuse. 
P = I*V
P = 35amperes*12 Volts
P = 420 Watts

Power = force x Distance/ Time

420 Watts = force x 1.22m/15s
420 Watts * 15s = force x 1.22m
6300 = force x 1.22 m
force = 5 163.93

Take into account the gear ration:
force = 5163.93/256
force = 20.17

Climbing Mechanism #2:

The climbing mechanism was a shaft 2" (5.08cm) in diameter powered by two mini-cim motors with a 42:1 gear reduction.
Mini CIM motor curve

Mini CIM Motor Specifications

 Free speed (RPM)6200 The maximum speed at which a motor will rotate when under no load
 Free Current (A)  1.5The minimum current a motor will draw when under no load
 Stall Torque (N ∙ m) 1.4The amount of load placed on a motor that will cause it to stall (stop moving)
Stall Current (A) 86The amount of current drawn by a motor when it is stalled

Formulas

Electrical:
P = I*V
P - Power in Watts
I - current in amperes (or amps)
V - electric potential in Volts

Mechanical:
Torque = Force * Distance or Force = Torque/Distance

Work = force x Distance

Power = Work/Time

Calculations

Our robot uses a 12 Volt battery and the fuse for the motor circuit is rated at 40 amps - we want to ensure we are only using 35 amps to not risk tripping the fuse. 
P = I*V
P = 35amperes*12 Volts
P = 420 Watts

Power = force x Distance/ Time

420 Watts = force x 1.22m/15s
420 Watts * 15s = force x 1.22m
6300 = force x 1.22 m
force = 5 163.93


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