robot dynamics
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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
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)
))(2( rpmrv
rnceCircumfere 2
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:
inchesorftdrpsdrpmrv
89.657.0)67.1(3))(2(
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 datasheet• motor torque
• motor speed
Motor Torque and Force / AccelerationHigh force is required to push other robots around, or to go up hills, or have high acceleration.
rF
Acceleration
maF
rpsorrpm Robot mass
Robot Motor Factor, RMFSomething to make life simpler, Can do quick calculation to optimize your robot or select the appropriate motor for your needs
)()(
2
vmarpsrpsrmarps
rF
RMF(depends on motor specs)
Robot characteristicsor requirements
))(2( rpmrv Wheel speed
Robot Motor Factor, RMFExample: You found the following 3 motorsMotor A: 2 ft lb, 1 rpsMotor B: 2.5 ft lb, 2 rpsMotor C: 2 ft lb, 4 rps
rpsRMF
RMFA= 2 ft lb rpsRMFB= 5 ft lb rpsRMFC= 8 ft lb 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
rpslbftRMFmaRMF v
77.4)2/(325)( 2
Motor B & C will both work. Motor C is overkill, waste of $Wheel
diameter to use?
inftrpsvd 73.548.0
)2(3
Robot EfficiencyRMF 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%
%)63(63.0)10.01)(30.01( Efficiency
Example: Tank robot on rough terrain would have what efficiency?
Robot Motor Factor, RMFincorporating efficiency
Something to make life simpler, Can do quick calculation to optimize your robot or select the appropriate motor for your needs
))(( 12 efficiencyvmarps
RMF(depends on motor
specs)Robot characteristics
or requirements(efficiency is a decimal # ie 80% is 0.8)
Link to RMF Calculator
Robot Arm Torquedetermine the torque required at any given lifting joint (raising the arm vertically) in a robotic arm
LmgLF
Weight of loadTorque
needed to hold a mass a given distance from a pivot L is the
PERPENDICULAR length from pivot to force
Robot Arm TorqueTo estimate the torque required at each joint, we must choose the worst case scenario
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
Greatest torque
Robot Arm Torque
Load
)2/()2/()(
1
1
WmgLLWLmg
WL=mgW1
L
L/2
)/1)()(2/1( efficiencyrpsWmgLrps
Arm weight
You must also add the torque imposed by the arm itself
RMF (motor specs)
Robot arm torque
WL=mg W3
L3
L3/2
Mot
or2
W2
L2L2/2
W1
L1
L1/2
Wm3
Wm2M
otor
3 Mot
or1
Wm1
Robot Arm Torque
)2/()( 3333 LWLmg
If your arm has multiple points, you must determine the torque around each joint to select the appropriate motor
)()()()( 222322323223 L
mL WLWLWLLmg
)()()(
)()()(2112212
2132213123112
3
Lm
Lm
L
WLWLWLLWLLWLLLmg
Robot Arm Torque
Link to Robot Arm Calculator
WL=mg W3
L3
L3/2
Mot
or2
W2
L2L2/2
W1
L1
L1/2
Wm3
Wm2M
otor
3 Mot
or1
Wm1
GearsNo 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:
newnewoldold vv Motor specs
Example: Suppose your motor outputs, according to spec are 3 lb-in torque at 2000rps ,but you only want 300rps. 3 lb-in * 2000rps = Torque_New * 300rps 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 necessary equations beforehand, will always save you tons of money and time.
3newnewoldold vv
Moves slowerMore torque
Moves fasterLess torque
Gear RatiosHOW do you mechanically swap torque and velocity with gears?
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 RatiosExample: 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 = 2/3new=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.