ROBOT DYNAMICS MOTORS supply the FORCE that the robot needs to move Rotational Force is called TORQUE The motor needs to supply force to • wheels • arms The Rolling of WHEELS without slipping or spinning Circum ference 2r Everytime a wheel rotates an entire revolution, the robot travels a distance equal to the circumference of the wheel. Multiply that distance by the number of rotations per minute (rpm) and you get the distance your robot travels in a minute (its speed) v (2r )(rpm) For example, if your motor has a rotation speed (under load) of 100rpm (determined by looking up the motor part number online) and you want your robot to travel at 3 feet per second, calculate the wheel diameter you would need: v (2r )(rpm) 3 d (1.67rps) d 0.57 ft or 6.89inches Wheel diameter and the motor rpm are not the only factors that determine robot velocity: • motor torque • robot weight • robot acceleration To achieve proper velocity/movement, you must balance • motor torque • robot acceleration • wheel diameter Motor Torque and Force / Acceleration High force is required to push other robots around, or to go up hills, or have high acceleration. Motor datasheet motor torque • • F r Acceleration F ma motor speed rpm or rps Robot mass Robot Motor Factor, RMF Something to make life simpler, Can do quick calculation to optimize your robot or select the appropriate motor for your needs F r rps m a(r rps) Wheel speed v v (2r )(rpm) rps m a( 2 ) RMF (depends on motor specs) Robot characteristics or requirements Robot Motor Factor, RMF Example: You found the following 3 motors Motor A: 2 ft lb, 1 rps Motor B: 2.5 ft lb, 2 rps Motor C: 2 ft lb, 4 rps RMFA= 2 ft lb rps RMFB= 5 ft lb rps RMFC= 8 ft lb rps RMF rps Suppose you want a velocity of 3 ft/s, an acceleration of 2 ft/s2, and you estimate your robot to weigh 5 lbs RMF ma ( v 2 ) 5 2 3 /(2 ) RMF 4.77 ft lb rps Motor B & C will both work. Motor C is overkill, waste of $ Wheel diameter to use? v 3 d 0.48 ft 5.73in rps (2) Robot Efficiency RMF is for 100% efficient systems. Gearing and friction and many other factors cause inefficiency. General rules for estimating inefficiency – If your robot • has external gearing, reduce efficiency 15% • uses treads, reduce efficiency 30% • operates on high friction terrain, reduce efficiency 10% Example: Tank robot on rough terrain would have what efficiency? Efficiency (1 0.30)(1 0.10) 0.63 (63%) Robot Motor Factor, RMF incorporating efficiency Something to make life simpler, Can do quick calculation to optimize your robot or select the appropriate motor for your needs rps ma( v 2 )( 1efficiency) RMF (depends on motor specs) Link to RMF Calculator Robot characteristics or requirements (efficiency is a decimal # ie 80% is 0.8) Robot Arm Torque determine the torque required at any given lifting joint (raising the arm vertically) in a robotic arm FL mg L Weight of load Torque needed to hold a mass a given distance from a pivot L is the PERPENDICULAR length from pivot to force Robot Arm Torque To estimate the torque required at each joint, we must choose the worst case scenario Greatest torque As arm is rotated clockwise, L, the perpendicular distance decreases from L3 to L1 (L1=0). Therefore the greatest torque is at L3 (F does not change) and torque is zero at L1. Motors are subjected to the highest torque when the arm is stretched out horizontally Robot Arm Torque You must also add the torque imposed by the arm itself L Load WL=mg L/2 W1 Arm weight (m g L) (W1 L / 2) L(m g W1 / 2) RMF (motor specs) Robot arm torque rps L(mg W1 / 2)(rps)(1 / efficiency) Robot Arm Torque If your arm has multiple points, you must determine the torque around each joint to select the appropriate motor L3 L2 L2/2 L3/2 WL=mg L1 W3 L1/2 Wm2 W2 Wm3 W1 Wm1 3 (mg L3 ) (W3 L3 / 2) 2 mg (L3 L2 ) W3 (L2 L 2 ) (Wm3 L2 ) (W2 L 2 ) 3 2 1 m g ( L3 L2 L1 ) W3 ( L1 L2 L 2 ) Wm3 ( L1 L2 ) 3 W2 ( L1 L2 2 ) (Wm 2 L1 ) (W1 L1 2 ) Robot Arm Torque L3 L2 L2/2 L3/2 WL=mg L1 W3 W2 L1/2 Wm2 W1 Wm3 Link to Robot Arm Calculator Wm1 Gears No good robot can be built without gears. Gears work on the principle of mechanical advantage With gears, you will exchange the high velocity of motors with a better torque. This exchange happens with a very simple equation that you can calculate: old vold new vnew Motor specs Example: Suppose your motor outputs, according to spec are 3 lb-in torque at 2000rps , v v old old new new but you only want 300rps. 3 lb-in * 2000rps = Torque_New * 300rps 3 new torque will be 20 lb-in. Now suppose, with the same motor, you need 5 lb-in of torque. But suppose you also need 1500rps minimum velocity. How do you know if the motor is up to spec and can do this? Easy . . . 3 lb-in * 2000rps = 5 lb-in * Velocitynew_ New Velocity = 1200rps You now have just determined that at 1200 rps the selected motor is not up to spec. Using the simple equation, you have just saved yourself tons of money on a motor that would have never worked. Designing your robot, and doing all the Gear Ratios HOW do you mechanically swap torque and velocity with gears? Moves slower More torque Moves faster Less torque The gearing ratio is the value at which you change your velocity and torque. It has a very simple equation. The gearing ratio is just a fraction which you multiple your velocity and torque by. Suppose your gearing ratio is 3/1. This would mean you would multiple your torque by 3 and your velocity by the inverse, or 1/3. Gear Ratios Example: Suppose you have a motor with output of 10 lb in and 100 rps (old=10 lb in, vold=100rps) and you have a gear ratio of 2/3 Gearing ratio = 2/3 new=10 lb in x 2/3 = 6.7 lb in vnew=100rps x 3/2 = 150 rps Building your First Robot (for beginners) 1. Design! Plan out everything on paper or computer (what material you will use, where to put every screw, how to attach sensors. Draw to dimension, mark holes and understand how the parts connect) 1. Keep it simple, look at other robots for design ideas. Don’t get imaginative or creative with your first robot. Use fewer and simpler parts 2.