ndzied1
Lifetime Supporting Member
I was having one of our new Sales Engineers work on a timing study for movement of a table and he said he would get a much faster move with a triangular motion profile vs. a traditional 1/3, 1/3, 1/3 trapazoidal motion.
The triangular move has a constant acceleration for the first half of the move time and a constant deceleration for the second half of the move time. In the traditional 1/3, 1/3, 1/3 trapazoid move, there is a constant acceleration for 1/3 of the move time, then movement at a constant velocity for 1/3 of the move time and finally, a constant deceleration for 1/3 of the move time.
These motion profiles are shown in the graphs below:
For the system we were working on, the actuator has a maximum acceleration of 0.3g where g=9.81 m/s^2. The move in question was a 24" move.
Bonus Questions:
The triangular move has a constant acceleration for the first half of the move time and a constant deceleration for the second half of the move time. In the traditional 1/3, 1/3, 1/3 trapazoid move, there is a constant acceleration for 1/3 of the move time, then movement at a constant velocity for 1/3 of the move time and finally, a constant deceleration for 1/3 of the move time.
These motion profiles are shown in the graphs below:
For the system we were working on, the actuator has a maximum acceleration of 0.3g where g=9.81 m/s^2. The move in question was a 24" move.
- Using the maximum acceleration and distance given, how much faster is the triangle move vs. the 1/3 trapazoid?
- What is the general formula for the time of a triangular move given an acceleration and distance?
- What is the general formula for the time of a 1/3 trapazoidal move given an acceleration and distance?
Bonus Questions:
- What is the ratio of Time required for a 1/3 Trapazoid move vs. the time required for an equivalent Triangular move (i.e. same acceleration and distance)?
- What is the ratio of maximum velocity achieved in the Triangular move vs. maximum velocity achieved in the 1/3 trapazoidal move?
- For the Trapazoidal move,
- What percentage of the total distance is traveled during the acceleration part of the motion?
- What percentage of the total distance is traveled during the constant velocity part of the motion?
- Explain how you can determine the above two percentages without using the equations: x=(1/2)*a*(t^2) or x=v*t. (where x is distance, a is acceleration, v is velocity and t is time).