2. MOTORS supply the FORCE that the
robot needs to move
Rotational Force is called TORQUE
The motor needs to supply force to
• wheels
• arms
3. 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
( rpm
r
v
r
nce
Circumfere
2
4. 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:
inches
or
ft
d
rps
d
rpm
r
v
89
.
6
57
.
0
)
67
.
1
(
3
)
)(
2
(
5. 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
6. Motor datasheet
• motor torque
• motor speed
Motor Torque and Force / Acceleration
High force is required to push other robots around,
or to go up hills, or have high acceleration.
r
F
Acceleration
ma
F
rps
or
rpm Robot mass
7. 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
)
(
)
(
2
v
ma
rps
rps
r
ma
rps
r
F
RMF
(depends on motor specs)
Robot characteristics
or requirements
)
)(
2
( rpm
r
v
Wheel speed
8. 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
rps
RMF
RMFA= 2 ft lb rps
RMFB= 5 ft lb rps
RMFC= 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
rps
lb
ft
RMF
ma
RMF v
77
.
4
)
2
/(
3
2
5
)
( 2
Motor B & C will both work. Motor C is overkill, waste of $
Wheel diameter
to use?
in
ft
rps
v
d 73
.
5
48
.
0
)
2
(
3
9. 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%
%)
63
(
63
.
0
)
10
.
0
1
)(
30
.
0
1
(
Efficiency
Example: Tank robot on rough terrain would have
what efficiency?
10. 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
)
)(
( 1
2 efficiency
v
ma
rps
RMF
(depends on motor specs) Robot characteristics
or requirements
(efficiency is a decimal # ie 80% is 0.8)
Link to RMF Calculator
11. Robot Arm Torque
determine the torque required at any given lifting
joint (raising the arm vertically) in a robotic arm
L
mg
L
F
Weight
of load
Torque
needed to hold a mass a given
distance from a pivot
L is the PERPENDICULAR
length from pivot to force
12. Robot Arm Torque
To 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
14. WL=mg
W3
L3
L3/2
W2
L2
L2/2
W1
L1
L1/2
Wm3
Wm2
Wm1
Robot Arm Torque
)
2
/
(
)
( 3
3
3
3 L
W
L
mg
If your arm has multiple points, you must determine the torque
around each joint to select the appropriate motor
)
(
)
(
)
(
)
( 2
2
2
3
2
2
3
2
3
2
2
3 L
m
L
W
L
W
L
W
L
L
mg
)
(
)
(
)
(
)
(
)
(
)
(
2
1
1
2
2
1
2
2
1
3
2
2
1
3
1
2
3
1
1
2
3
L
m
L
m
L
W
L
W
L
W
L
L
W
L
L
W
L
L
L
mg
15. Robot Arm Torque
Link to Robot Arm Calculator
WL=mg
W3
L3
L3/2
W2
L2
L2/2
W1
L1
L1/2
Wm3
Wm2
Wm1
16. 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:
new
new
old
old v
v
Motor specs
17. 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
3
new
new
old
old v
v
18. Moves slower
More torque
Moves faster
Less torque
Gear Ratios
HOW 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.
19. 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
20.
21.
22. 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.
Editor's Notes
Talk about how to design robot with an understanding of the forces required to move it
Understand what forces are required can use the right motors and gears
First talk about the force needed for the wheels to move the robot
We all know what velocity is, but how do you design a robot to go at a defined velocity? Of course you can put a really fast motor on your robot and hope that it will go fast enough. But if you can calculate it you can design it to go your required speed without doubt, and leave the rest of the motor force for torque. So how to do this?
Wheel diameter. When buying (or making) your wheels you want to put your motor into consideration. For a start, there is torque and velocity. Large diameter wheels give your robot low torque but high velocity. So if you already have a very strong motor, then you can use wheels with larger diameters. Servo's already have good torque, so you should use larger diameter wheels. But if your motor is weak (such as if it does not have any gearing), you want to use a much smaller diameter wheel. This will make your robot slower, but at least it has enough torque to go up a hill! Another dumb mistake someone can make is buying a wheel that has a diameter close to or less than the motor diameter. For example, if you have a 1" diameter motor, and a 1.5" diameter wheel,
The larger the diameter of the wheel or the higher the rpm, the faster the robot will go
But this not entirely true in that there is another factor involved. If your robot requires more torque than it can give, it will go slower than you calculated. Heavier robots will go slower. Now what you need to do is compare the motor torque, your robot acceleration, and wheel diameter. These three attributes will have to be balanced to achieve proper torque.
But you also want to be concerned with acceleration. For a typical robot on flat terrain, you probably want acceleration to be about half of your max velocity.
by looking at the motor datasheet you can determine the output velocity and torque of your motor. But unfortunately for robots, motors commercially available do not normally have a desirable speed to torque ratio (the main exception being servos and high torque motors with built in gearboxes). For example, do you really want your robot wheels to rotate at 10,000 rpm at low torques? In robotics, torque is better than speed.
But you also want to be concerned with acceleration. For a typical robot on flat terrain, you probably want acceleration to be about half of your max velocity.
So this means you need a motor with an RMF greater or equal to 4.77
RMF is only for 100% efficient system. In reality this never happens.
GEARING and FRICTION and many other factors cause inefficiency
Eg if tank robot on rough terrain would have efficiency of (100-30)(100-10)=
Although the above equations are intended for robot wheels, they will also work for any other robot part. If you were say designing a robot arm, instead of using diameter use robot arm length. Then you can calculate how fast the arm will move with a certain weight being carried, for example
2nd – force required to move robot arm. Use L instead of r
The point of doing force calculations is for motor selection
Use L instead of r
Must add torque imposed by the arm itself (assume its weight at middle of bar)
Add any weight as a result of the robot arm's weight. If the robot arm itself weighs 100 pounds, and the arm is uniform, its center of gravity can be considered to be at the middle of the arm,
Note: if any of the joints have two or more motors, they share the torque required evenly. Because the base of the arm is subjected to the highest torque, often two actuators are used instead of one
Use L instead of r
Must add torque imposed by the arm itself (assume its weight at middle of bar)
Add any weight as a result of the robot arm's weight. If the robot arm itself weighs 100 pounds, and the arm is uniform, its center of gravity can be considered to be at the middle of the arm,
Note: if any of the joints have two or more motors, they share the torque required evenly. Because the base of the arm is subjected to the highest torque, often two actuators are used instead of one
Torque around each motor
Keep the heaviest components, such as motors, as close to the robot arm base as possible. It might be a good idea for the middle arm joint to be chain/belt driven by a motor located at the base (to keep the heavy motor on the base and off the arm).
unfortunately for robots, motors commercially available do not normally have a desirable speed to torque ratio (the main exception being servos and high torque motors with built in gearboxes). For example, do you really want your robot wheels to rotate at 10,000 rpm at low torques? In robotics, torque is better than speed.
Gears work on the principle of mechanical advantage. This means that by using different gear diameters, you can exchange between rotational (or translation) velocity and torque. by looking at the motor datasheet you can determine the output velocity and torque of your motor. But unfortunately for robots, motors commercially available do not normally have a desirable speed to torque ratio (the main exception being servos and high torque motors with built in gearboxes). For example, do you really want your robot wheels to rotate at 10,000 rpm at low torques? In robotics, torque is better than speed.
Bigger the size difference (gear ratio), the greater the difference in speed and torque
More accurate way to determine gear ratio is ratio of gear teeth
Bigger the size difference (gear ratio), the greater the difference in speed and torque
Unfortunately, by using gears, you lower your input to output power efficiency. This is due to obvious things such as friction, misalignment of pressure angles, lubrication, gear backlash (spacing between meshed gear teeth between two gears) and angular momentum, etc. Different gear setups, different types of gears, different gear materials, and wear and tear on the gear, will all have different efficiencies
Design When I first started building my first robot, someone much more experienced than me once said paraphrased, "if you build a mechanically crappy robot with expert programming and control, you will only get a crappy robot; build a mechanically professional robot with crappy programming and control, you will still get a well built robot." Its very good advice which I still use today.
I cannot emphasize any more for you to design your robot out on paper (or computer) first. This means plan out everything, such as what material to build your robot out of<, where to put every screw, how you will attach your sensors - EVERYTHING. You will save money and time, and will have a better constructed robot too. To do this, you should draw all your parts out to dimension, mark your holes, and understand how all your parts connect.
