ROBOT DYNAMICS

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.