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  • Writer's pictureLaurens Roos

Kit robot part 4; belts, chains, pullies and a whole lot more.

In the last post we talked about designing a transmission/actuator unit, now to actually move something with this unit, or design something that it can move. I am still waiting for the parts to assemble the transmission and test it out. Once they arrive I tune the design based on the parts and assemble. But for now lets continue on the design for the first joint of our robot; the base rotation. This will hold all the weight of the whole robot and will have to move 360 degrees. (ideally more) So the first question is; how to transmit the output of our actuator to our joint? (no not that joint you fill with grass)


Gears vs Belts vs chains

To transmit the power we have three options (because all great things come in 3 from game quests to the amount of tries something takes to work) each of the drives have their own advantages and disadvantages so the first step is to make a list of requirements to choice the drive on;

  • great for 3D printing/laser cutting without the need to buy expensive parts or CNC mill.

  • effective at transmitting the power

  • non-slip

  • low maintenance / robust

1: The humble gear drive

Perhaps as old as tool making, or if we look at nature even older. Gears are a simple and effective way of transmitting mechanical motion. There are simply a lot of tooth profiles and each have their advantages and disadvantages. The easiest profile to imagine is a square tooth but this tooth is inefficient in transmitting any load. I am going to skip the long and complicated history of gears (I will perhaps save that for another time). The current design most often used is an involute gear this profile makes sure to have constant contact on the gears without shifting or speed variations with an optimal load profile. This gear profile is a bit tricky to make but is doable. If an high enough module is selected it will be fine in 3D printing. Other techniques are cutting them on an indexing plate with gear cutters or gear hobbing. Techniques involving rather expensive machinery and tools.


The major down side of a gear I see if that the load of the transmission only rests on a few teeth. Since we have a differential drive in our robot, gears will be unavoidable, but we cross that bridge when we come there. Another side effect I see is that they have a larger pinching hazard, not a deal breaker but for anything easily reachable I do want to avoid pinching. They can also be rather messy with the needy to have adequate lubrication along the gears.

2: heavy metal and chains

Cruising down the high way on your motor, its the chain that makes sure the torque meets the rubber. High strengths and don't stretch, the chain in one way or another is always involves in high torque applications. Trough the current application is not high torque enough to consider a chain drive. They are also rather heavy and require lubrication along the whole chain. This leaves us all with;

3: A timely belt.

Belts are differentiated into timing belts and V-belts. Since V-belts are mostly used for power transmission where slip is not a big deal, like the water pump of a car, the slip could even be a safety feature, like with a wood turning lathe where the slip of the belt reduces the injury when something goes wrong. But for the operation of the robot we need to have the position between the actuator and the joint to be static. Thus a timing belt is best.

For timing belts there are two versions; trapezoidal and round. The round version is also called HTD belts or high torque drive belts. The name itself suggest the application of these belts. Further more a HTD belt has less of a backlash (around 0.03 mm) then a trapezoidal belt (around 0.2 mm).

I will be using a HTD belt for that extra accuracy in positioning. However an trapezoidal belt is a good alternative if it is easier to source/machine for you. (but I expect 3D printers to be able to print a round profile of a HTD belt more easily then a sharp edged trapezoidal belt)

4; I miss directed about a 4th option.

The forth option would be direct drive mount the output of the motor shaft directly to axis. This has no transmission losses or slippage between the actuator and the joint. But this comes with space constraints. Technically direct drive doesn't exist in this robot since all motors have a reduction simply due to the fact the robot desires low speeds high torque.

Designing the belt.

With a tooth belt chosen as the option its time to select our profile. Due to the constrains we discussed in the belts section we already selected an round or M-profile belt. Now the pitch to be selected is a combination of the calculated power, load and what the way of the pulley is constructed. Time to design out drive for the joints in 12 steps.


  1. Calculate the correction factor with the formula Cc = Vs + Cm +Cf

First off in the formula is the Vs or Safety factor, this depends on the type of machine and goes according with the following two tables.


Motor Class

Class I

Class II

Class III

Peak load in % of nominal load

0-149%

150-249%

250-400%

Single phase motor

Every single phase motor

Tri-phase motor

Star/delta start

direct run-up

Slip-ring anchor

Synchoonous motor

norm torque

high torque

DC-motors

Shunt

Compound

Serial

Combusion motors

from 8 cylinders

6 cylinders

t/m 4 cylinders

Hydraulic motors

All

The expected class of our Brushless DC motor will be a class II, Brushless DC motor acts like a tri-phase motor with a controller that does the run-up for us. We expect high peak loads due to a dynamic design that is back drivable, with the motor class we can select the Factor of safety.

Type of machines

Class I

Class II

Class II

Bakerymachines, doughmachines

1.4

1.6

1.8

Centrifuges

1.7

1.9

-

Compressors; Piston

Centrifugal

2.0

1.6

2.2

1.7

2.4

1.8

Printing-machines:

printing-machines, rotation-presses, Linotypes, fold and cutting machines

1.4

1.6

1.8

Driveshafts

1.4

1.6

1.8

Generators and dynamo's

1.6

1.8

2.0

Hammer mills

1.7

1.9

2.1

Wood-industry: Rotation-Machines, Band-saws

circular saws, planer

1.3

1.4

1.4

1.6

-

Wood-sawing-machines

1.6

1.8

2.0

Elevators, Hoists

1,6

1,8

2,0

Mills; Ball-, Bar-, Cone-

2,2

2,5

-

Paper-machines; Stirring machines, Calenders, Dryer

Strokemill, Nash-pumps, Pulp-machines

1,4

1,7

1,6

1,9

1,8

2,1

Pumps: Centrifugal, Gear, rotary:

Pump-line

suction-line

----------

1,5

2,0

----------

1,7

1,9

-----------

1,9

2,4

Agitators, mixing-machines (with screw or blades):

Liquid

Semi Liquid

--------

1,4

1,5

---------

1,6

1,7

---------

1,8

1,9

Rubber-machines

1,6

1,8

2,0

Stone-works: Mixers and granulators

kollergangen, Kneeding machines

1,5

1,8

1,8

2,0

1,9

2,2

Textile machines: Weaving-, spin-, twine-machines

Wrap, threating-machines

1,6

1,5

1,8

1,7

2,0

-

Transporters; -Light band transporters, ovens

-Heavy brand transporters; ores, coal, zand

-Slat-, Chain-, Beam-Conveyors

1,3

1,6

1,7

1,5

1,7

1,8

1,7

1,8

1,9

Ventilators, blowers:

- Centrifugal, exhausters with inductive pulls

- Screw-, mine-ventilators, postive blowers, forced pull

-------

1,6

1,8

------

1,8

2,0

------

2,0

2,2

laundry machines: General

Washingmachines

1,5

1,6

1,6

1,8

1,7

2,0

Machine tools: Lathes, Threading machines

Drill-, Grinding-, Gear Milling-machine

1,4

1,5

1,6

1,7

1,8

1,9

sieving machine: Vibration sieve, Shaking sieve

Barrel sieve, conical sieve

1,5

1,4

1,7

1,5

-

-

Since robots is not a known category we must match the robotics to one of the categories in the table. Two categories come close; Machine tools and Drive shafts. Luckily both categories have the same Factor of Safety; 1,6 for class II engines. Now we have two safety factors left; Cm, Cf which follow the following table:


Transmission ratio

Factor Cm

from 1 to 0,806

0

from 0,806 to 0,575

+0,1

from 0,575 to 0,402

+0,2

from 0,402 to 0,286

+0,3

under 0,286

+0,4

operating hours per 24 hours

Factor Cf

8-10 hours continues

0

10-16 hours continues

+0,1

16-24 hours continues

+0,2

With tensioner

+0,1

Intermittent operation

-0,1

So before we can definitely determine our transmission, we need to desire what design parameters our transmission will have. First off is our main pulley or the one driving the joint. Due to the size of the joint (this will be clear later) this is around an 145 teeth pulley the drive pulley will be around 29 teeth to give an 1-5 transmission or and ratio of 0,2 which has an Cm penalty of 0,4. the operational hours is a bit harder to decide. The robot will have an designed operation of 8 hours but will have belt tensioners to take make the belt fit in better. this leaves an Cf of 0,1.

With all this we can finally calculate the correction factor; C = 1,6 + 0,4 + 0,1 = 2,1

so time for step two;

2. calculate the corrected power with P = C*p;

the motor power is 40 amp 24 V max, there are transmission losses and driver losses. But i will assume that will all be delivered to the motor, this means that our corrected power is:

P = 2,1 * 40 * 24 = 2016 Watt

3. Select our toothed belt pitch.

The graph needed can be found in the book "Transfer W Tabellen en Formules" ISBN 9789006900392, I sadly don't know how to share this graph, which is an graph with the pitches per rpm and power. What i will share is an table with the rpm our robot has (around 60 rpm) and the ranges of pitch.


Type

Pitch

Usage

Examples of applications

power range (100 rpm)

XL

1/5" (5,080 mm)

Ultra light

Labatory intruments, sewingmachines, small filming equiptment, writing machines, small 3D printers

-

L

3/8" (9,525 mm)

Light

Small pumps, mixers, sandingmachines, small tools, washingmachines, larger 3D printers

0,1-0,2 kW

H

1/2" (12,7 mm)

Middle - heavy

Tools, Compressors, Textile machines, generators, transmission

0,2 - 2 kW

XH

7/8" (22,225 mm)

Heavy

Diesel-generators, ventilators, piston comrpessors, mixers

2 - 5 kW

XXH

1 1/4" (31,750 mm)

Extra Heavy

Presses, conveyors, stone breakers, Press-rollers

5 - 10,5 kW

The belt is an type H pitch belt giving us a range of selection of an H5M belt. (We want a higher belt pitch then needed to make sure the teeth of the gear will not get damaged due to the load.) I will give an example on how to draw the pulley based on the small pulley but first we need one extra step for the pulley;


4. Select the minimum amount of teeth;

This is far easier, we know our rpm, we know our belt, so we can just look at the following table

Teeth pitch

RPM

Min. Dw (mm)

Min. teeth

XL

-3000

-1500

-1000

19,40

17,79

16,17

12

11

10

L

-3000

-1500

-1000

48,51

42,45

36,38

16

14

12

H

-3000

-1500

-1000

80,85

72,77

64,68

20

18

16

XH

-1500

-1000

- 750

183,94

169,79

155,64

26

24

22

XXH

- 1500

- 1000

- 750

262,76

242,55

222,34

26

24

22

So 16 teeth is our minimum design spec for a gear. a 29 gear pulley will be in spec. further more its time to see if we can source our part. A look at McMaster-carr gives us plenty of belts with the type H5M in the width of 9, 15 and 25 mm.


5. Decide the transmission ratio

This one is simple and it what ever you want it to be with the contains of minium of teeth, this comes to 1:5 for joint 1.


6. Decide the amount of teeth and Pulley centre lines.

We have two pulleys that decide the amount of teeth. The bigger pulley has the constraint that it needs to be large enough to fit on the bearing (200 mm) and thus will be 145 teeth. The other pulley then is derived from the large pulley by deciding with the transmission ratio; 145/5 = 29 teeth. with this we can design our pulleys as follows:

T vs M-profile

To design the m-profile pulley three variables are of important for the pulley itself and the forth value (Dw = Working Diameter) is for calculation purposes and derived from the first three values. The Hs (Height Belt), Ht (Height Teeth), and T (pitch) value are the same between a pulley and a belt design but the position changes. T value is the pitch of the profile. In this case 5 mm. For drawing a pulley the pitch is given on the centre lines of the teeth that intersects the Dw line. (the Dw line/circle is halfway between the Ht line and Hs line)


upclose image of the Dw cirkle compaired with the Hs and Ht

The Hs variable is the outside of the belt and the Ht is the height of the of the teeth. In the table below the given sizes for T and M-profiles are given










Type

T

Hs

Ht

S

β

Type

T

Hs

Ht

T 2,5

2,5

1,3

0,7

1,5

40°

3M

3

2,4

1,2

T5

5

2,2

1,2

2,65

40°

5M

5

3,6

2,1

T10

10

4,5

2,5

5,30

40°

8M

8

5,6

3,38

T20

20

9,1

5,0

10,6

40°

14M

14

10,0

6,1

20M

20

13,2

8,4

Below is the design for both pulleys with the Dw measurement needed for the rest of the calculations.


7. Decide the temporary heart line.

This can be whatever you want it to be, what fits best for the design, for now I choice 190 mm to give enough space between the components.

8. Calculate the temporary belt length

Hold on this is going to be quite some formula.

Ib = 2*hv + 1,57 * (Dw + dw) + (Dw+dw)²/(4*hv)

where:

  • Ib = belt length

  • hv = heart line

  • Dw = working diameter big pulley

  • dw = working diameter small pulley

so with all the info given:

Ib = 2*190 + 1,57 *(230,59=46,25)+(230,59+46,25)²/(4*190) = 915,48 mm


9. Define the definitive heart distance;

First we look at the available belts; we have the choice between the following belts:

  • 800-5M

  • 900-5M

  • 1000-5M

perhaps now its a best time to talk about belt product numbers. this is luckily standardized between manufacturers and follows the formula of; "lenght-profile-width"

so an 800-5M-9 belt has a length of 800, profile of 5M (m-profile pitch 5 mm) and a width of 9 mm. if you want an similar belt in t-profile that would be an 800-T5-9.


for the robot a definitive belt length of 900 is perfect, now to adjust the heart length between the pulleys to match the belt. The formula used is h = hv + (l-lb)/2

so 190 + (900-915,48)/2 = 182,26 mm.

We adjust the design and check for collisions.

If there is a design issue, a bigger belt can be selected, sometimes additional idlers have to be used to shorten the belt. Idlers can also be used to tension the belt.

but with everything being.

The last thing we have to decide is the width of the belt;


9. Calculate the teeth in engagement.

and another formula.

zi = (0,5 - (4*t)/(79*h)*(z2-z1))*z1

where:


  • t = teeth pitch

  • h = heart distance

  • z1 = teeth small pulley

  • z2 = teeth big pulley

so

zi = (0,5 - (4*5)/(79*182,26)*(145-29))*29 = 9,87 teeth in engagement.


11 . Calculate the belt width factor

the formula for this is

C1 = Pc / (Cd * Pb)

where


  • C1 =belt width factor

  • Pc = corrected power (calculated in step 2 being 2kw)

  • Cd= engagement-factor

  • Pb = Power per inch belt width. (why inch, no clue. I thought we where doing metric here dammit, but I will roll with it)

first off to select the engagement factor with the following table;


Amount of teeth in engagement

Factor Cd

>6

1,00

5

0,8

4

0,6

3

0,4

2

0,2

the Cd is 1,00


The Pd is harder to select and depends on the type of belt and the rpm, this table can be found in the book Transfer W; Tabellen en formules.

29 teeth will be an Pb of 6,6 kw/inch

so C1 = 2/(1*6,66) = 0,30


12. choice the width

we have finally arrived at the end, choice the width of the belt, this can be done with the following table:


Factor Cf

belt width code

teeth belt mm

teeth belt inches

0,18

025

6,4

1/4"

0,23

031

7,9

5/16"

0,30

037*

9,7

3/8"

0,37

044

11,1

7/16"

0,45

050*

12,7

1/2"

0,60

062

15,9

5/8"

0,72

075*

19,1

3/4"

0,87

088

22,2

7/8"

1,01

100*

25,5

1

our belt width is 037, or 9,7 mm or 3/8" The one problem is that the belts available in metric here are 9 or 15 mm. To keep it compact, I will go for an 9 mm belt since I don't expect the max torque to be given for long period of time. But i will design the pulley to be easily exchangeable for an 15 mm pulley if the needs arises.


with that I will leave you all, Next blog post will be designing the first joint of the robot. I will not provide this step by step guide for each joint I design, only when needed. but I wanted to at least walk you trough the whole process for a toothed belt at least once to give you some help with your next project.

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