1. Find a smooth path for a robot joint that will turn from θ= 75° to θ = -35° in 10 seconds. Do this by developing an equation then calculating points every 1.0 seconds along the path for a total motion time of 10 seconds. Do not assume a maximum velocity.
2. Paths are to be planned for a three axis motion controller. Each of the joints has a maximum velocity of 20 deg/s, and a maximum acceleration of 30 deg/s/s. Assuming all of the joints start at an angle of 0 degrees. Joints 1, 2 and 3 move to 40 deg, 100deg and -50deg respectively. Develop the motion profiles assuming,
3. Develop a smooth velocity profile for moving a cutting tool that starts at 1000 inches and moves to -1000 inches. The maximum velocity is 100 in/s and the maximum acceleration is 50in/s/s.
4. An axis has a maximum velocity of 2.0 rad/s and a maximum acceleration/deceleration of 0.5 rad/s^2. Sketch a trapezoidal motion profile and find the motion time for a -4.0 rad motion.
5. An axis has a maximum velocity of 5m/s and an acceleration/deceleration time of 1s. Sketch a trapezoidal motion profile and find the motion time for a 25m motion.
6. Develop a smooth velocity profile for moving a cutting tool that starts at 1000 inches and moves to -1000 inches. The maximum velocity is 100 in/s and the maximum acceleration is 50in/s/s.