Pathfinder Chassis Spring 2019
Motor and Servo Torque Back of the Envelope Calculations
Author: Daniel Enverga (Mission, System, & Testing)
Approval: Alexandrea Jackson (Project Manager)
Table of Contents
Introduction
This blog post will focus on the back of the envelope calculations to determine whether the mechanical components of Pathfinder Chassis Generation 7 can be used to fulfill our mission. This will include RPM needed to achieve a desired mission time, torque necessary to move the Chassis, and torque necessary to move the Pan and Tilt system.
Mission Time
RPM can be determined by the following equation:
We can calculate the # of rotations needed by knowing the distance of the mission and the distance after one rotation of the wheels used.
We know that the diameter of our wheels are 6 inches (from generation 4) and the distance of the course is 0.09 miles which is 475.2 feet.
Now that we know the # of rotations needed, we can find the RPM needed to complete the course within our mission time, 35 minutes.
From these calculations we would need motors that would produce a RPM of at least 8.64 to for the Chassis to complete the mission course within 35 minutes.
Motor Torque
Torque could be determined by the equation
From Physics we can find the force needed to push the Chassis as this equation.
From the mass report we know the Chassis is 13.147 Kg. We can calculate the acceleration of the Chassis by using this equation.
With Force we can now determine the amount of torque needed.
We convert torque to kg cm since the motor datasheets show rated torque in kgcm.
Servo Torque (Pan & Tilt)
The servos for pan and tilt will be split into two different calculations because the servos will be controlling two different pieces of the system; the pan and tilt.
The tilt part of the system only contains the aluminum casing for the phone while the pan part of the system contains everything on the pan and tilt including the servo for the tilt. So we will start the calculations for the tilt system.
The aluminum case for the mobile phone weighs 31.1g and the diameter of the rotational part of the servo is 1.5 inches in which the circumference is the following.
The servos maximum speed is 0.2 sec / 60° which means every 0.2 sec the servo would rotate ⅙ the circle. We can find the distance per second (acceleration) by multiplying the distance traveled in 0.2 sec by 5.
By applying the previous equations to find force, we can also find the torque needed for the tilt system.
The pan system can be calculated the same way, except changing the overall mass to 513.1g and the diameter being 1 inch. Following the previous equations:
Conclusion
From our calculations we would need the run the Pathfinder Chassis at least 8.64 RPM to complete the mission in 35 minutes. Our motors fulfill this by the specification of the datasheet of 14 RPM. These same motors would need to supply a torque of at least 1.445 [kgcm] in which is also fulfilled since the motors are rated at 32 [kgcm]. The servos would need to operate at a torque of at least 0.0012044 kgcm. The servos data sheet verifies that the current servos are usable with a maximum torque of 9.6[kgcm].
These calculations can be also verified by a number of tests to determine whether the servos and motors are able to perform as expected.