Interpolation. Create a program for linear interpolation of a three axis manufacturing machine with a constant

Transcription

1 QUESTION 1 Create a program for linear interpolation of a three axis manufacturing machine with a constant velocity profile. The inputs are the initial and final positions, feed rate, and sample period. The outputs are the reference positions for all three axes. Test the code for an initial position of (10, 14, 58) mm, a final position of ( 26, 89, 39) mm, a feed rate of 50 mm/s, and a sample period of 10 ms. On separate graphs plot the individual axis reference positions as functions of time, individual axis reference velocities as functions of time, the reference positions in three dimensional space, and the reference velocity along the path as a function of time. QUESTION 2 Create a program for linear interpolation of a three axis manufacturing machine with a constant acceleration profile. The inputs are the initial and final positions, feed rate, and sample period. The outputs are the reference positions for all three axes. Test the code for an initial position of (10, 14, 58) mm, a final position of ( 26, 89, 39) mm, a feed rate of 50 mm/s, acceleration of 0.1 m/s 2, and a sample period of 10 s. On separate graphs plot the individual axis reference positions as functions of time, individual axis reference velocities as functions of time, the reference positions in three dimensional space, and the reference velocity along the path as a function of time.

2 QUESTION 3 Create a program for circular interpolation of a two axis manufacturing machine with a constant acceleration profile. The first circular arc has an initial position of (80,40) mm, final position of (40,80) mm, feed rate of 50 mm/s, acceleration of 0.1 m/s 2, radius of 40 mm, sample period of 0.01 sec, counterclockwise direction, and less than 180 o. The second circular arc has an initial position of (80,40) mm, final position of (40,80) mm, feed rate of 50 mm/s, acceleration of 0.1 m/s 2, radius of 40 mm, sample period of 10 ms, clockwise direction, and greater than 180. On separate graphs plot the individual axis reference positions as functions of time, individual axis reference velocities as functions of time, the reference positions in two dimensional space, the reference velocity along the path as a function of time, the angular displacement as a function of time, and the angular velocity as a function of time. QUESTION 4 For the constant jerk (i.e., the derivative of acceleration with respect to time) one dimensional interpolator shown in Figure 1, complete the following: a. Determine the equations for jerk, acceleration, velocity, and position during each of the three phases. The jerk is constant during Phase 1. Phase 1 is complete when the reference velocity reaches the commanded feed rate. During Phase 2, the reference velocity is constant and is equal to the commanded feed rate. The jerk is constant during Phase 3. At the beginning of Phase 3, the acceleration is negative of the acceleration at the end of Phase 1. Page 2

3 b. Determine the times when Phases 1 and 2 are complete. c. Create a program to implement the interpolator for a jerk magnitude of 4 mm/s 3, and feed rate of 2 mm/s, initial position of 0 mm, and a final position of 10 mm. d. Implement the interpolator for a jerk magnitude of 4 mm/s 3, and feed rate of 2 mm/s, initial position of 5 mm, and a final position of 5 mm. jerk acceleration velocity position time Figure 1 QUESTION 5 Create programs for real time linear interpolation of a three axis manufacturing machine with both constant velocity and constant acceleration profiles. The inputs are the initial and final positions, commanded feed rate, and sample period. The outputs are the reference positions for all three axes. Test the code for an initial position of (10, 14, 58) mm, a final position of ( 26, 89, 39) mm, acceleration of 0.1 m/s 2, and a sample period of 10 ms. The commanded feed rate Page 3

4 is 50sin(10t) mm/s. On separate graphs plot the individual axis reference positions as functions of time, individual axis reference velocities as functions of time, the reference positions in three dimensional space, and the reference velocity along the path and commanded feed rate as functions of time. QUESTION 6 Create programs for real time circular interpolation of a two axis manufacturing machine with both constant velocity and constant acceleration profiles. The first circular arc has an initial position of (80,40) mm, final position of (40,80) mm, feed rate of 50 mm/s, acceleration of 1 mm/s 2, radius of 40 mm, sample period of 10 ms, and counterclockwise direction. The second circular arc has an initial position of (80,40) mm, final position of (40,80) mm, acceleration of 1 mm/s 2, radius of 40 mm, sample period of 0.01 s, and clockwise direction. On separate graphs plot the individual axis reference positions as functions of time, individual axis reference velocities as functions of time, the reference positions in two dimensional space, and the reference velocity along the path and commanded feed rate as functions of time. QUESTION 7 For very short motion segments, a constant acceleration interpolator will not reach the commanded feed rate. Complete the following: a. Modify the one dimensional constant acceleration linear interpolator such that if the motion segment is too short to reach the commanded feed rate, the interpolator has only Page 4

5 two phases. During the first phase the feed rate is reduced such that at the end of the phase the reference position is half way between the initial and final positions. During the second phase, the acceleration is the negative of the acceleration during the first phase. b. Test the interpolator for an initial position of 1 mm, a final position of 2 mm, a feed rate of 2 mm/s, an acceleration of 1 mm/s 2, and a sample period of 10 ms. On separate graphs plot the axis reference acceleration, velocity, and position as functions of time. c. Test the interpolator for an initial position of 1 mm, a final position of 0 mm, a feed rate of 2 mm/s, an acceleration of 1 mm/s 2, and a sample period of 10 ms. On separate graphs plot the axis reference acceleration, velocity, and position as functions of time. Page 5