0
$\begingroup$

For a robotics project I wanted to find the optimal gear ratio for my robot to travel 10 meters. Unfortunately. the acceleration is nonconstant, and that proved to make my life much harder. I think I have most of it figured out, and the only part left is to find the correlation between the acceleration and velocity graph to the acceleration/velocity/position to time graph.

The robot with mass m and wheels that have a radius of r is allowed to accelerate on a surface with negligible friction. It uses 4 motors that have a free speed of Vfree rpm, and a stall torque of Tstall. The graph is included below. How can I find the time taken for this robot to travel x meters? I was able to turn the torque to angular velocity graph into an acceleration to velocity graph, but I got stuck trying to transform it into a distance to time or even a velocity to time graph.

angular velocity to torque graph

$\endgroup$

closed as off-topic by John Rennie, glS, JMac, ZeroTheHero, AccidentalFourierTransform Aug 30 '18 at 15:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question appears to be about engineering, which is the application of scientific knowledge to construct a solution to solve a specific problem. As such, it is off topic for this site, which deals with the science, whether theoretical or experimental, of how the natural world works. For more information, see this meta post." – John Rennie, glS, JMac, ZeroTheHero, AccidentalFourierTransform
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ If that helps, you may use $a=v\frac{dv}{ds}$ to find displacement. $a$ is acceleration, $v$ is velocity and $s$ is displacement. If displacement does not change direction, then it can be taken as distance too. $\endgroup$ – Jitendra Aug 26 '18 at 11:07
  • $\begingroup$ If you don't get an answer here in a few days, you may want to try over at Robotics where perhaps someone there has dealt with a similar issue. $\endgroup$ – Kyle Kanos Aug 26 '18 at 11:58
1
$\begingroup$

Your graph is a good start. You need to use the radius of the wheels to express the torque as a force at the road and express the rpm as velocity. Then you will have a force vs velocity diagram.

Then write Newton’s 2nd law as $$F(v)=m\;dv/dt$$ and solve the differential equation for $$v(t)$$. Then integrate velocity to get distance.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.