Real-Life Math
"It takes more than just math and physics. It takes good old plain
common sense."
That's how Neville Westrop sums up what it takes
to be a good robotics technologist. And he should know. After over 30 years
of working in the field, he's been a mentor to "more hopefuls than I
can remember, and the most successful ones have been similar in that respect.
They all have a basic understanding and curiosity about how things work. They
pay attention to the relationships in mechanical processes and they apply
what they learn in one area to problems in another area."
See if you
can solve this problem using your skills in math and physics and common sense.
You
work in an automated factory where a new robot has just been designed. The
robots have what are called hydraulic actuators for arms. These actuators
are pistons that move in and out of a cylindrical "sleeve." By pumping oil
either behind or in front of the piston, the actuator can move an object.
Your
responsibility is to buy the pump that works the hydraulic actuator-piston.
The pump must meet the pressure and flow rate specifications of the actuator.
You
call up your company's machinery and parts supplier. They send you a
list of the pumps they sell, along with the specifications for each.
Pump
A
Pressure capability = 206 lbs. per square inch
Flow
rate capability = 72 inches cubed per second
Pump
B
Pressure capability = 53 lbs. per square inch
Flow
rate capability = 19 inches cubed per second
Pump
C
Pressure capability = 96 lbs. per square inch
Flow
rate capability = 38 inches cubed per second
Using the
following information and formulas, determine the pressure and flow rate specifications
for the hydraulic actuator. From the supplier's list, choose the appropriate
pump.
Pressure
- The radius of the piston-actuator head is one inch
- The hydraulic actuator must exert a force of 300 lbs.
- F = force (lbs.)
- P = pressure (lbs. per square inch)
- A = area of actuator-piston head (pi x radius squared)
- Force = pressure x area
Flow Rate
- The hydraulic actuator is designed to move 12 inches in one second
- V = Velocity ( V = distance (inches) / time (seconds))
- Q = Flow rate inches cubed per second
- Q = V x A
Choose the appropriate pump from the list.