design of double stage cycloidal drive using roulette...

© June 2017 | IJIRT | Volume 4 Issue 1 | ISSN: 2349-6002

IJIRT 144594 INTERNATIONAL JOURNAL OF INNOVATIVE RESEARCH IN TECHNOLOGY 99

Design of Double stage cycloidal drive using roulette

curve generation technique.

Dr. K B Waghulde1, Mr. Agale V B2, Mr. Kamble A B3, Mr. Kale S S4, Mr. Bhandawale A V5 and Mr.

Jaiswal K N6 1Faculty guide, Mechanical Engineering, PVPIT, Bavdhan, Pune 21 2,3,4,5,6Student, Mechanical Engineering, PVPIT, Bavdhan, Pune 21

Abstract—Engineers have been working on building

efficiency of cyclo-drives, multi-staging of cycloidal

drives and attempting to test superior materials for

increasing its life-cycles. The speed reducer is a

mechanism where the speed of input to output shaft is

reduced by a certain ratio. The cycloidal speed reducer

is commonly used in RV-3SB series robotic joints. The

challenge lies in designing cycloidal speed reducer

without exceeding the contact stress limit of rollers and

disc. The authors have worked on design of cycloidal

reducer and its geometry. The design literature

regarding double stage cycloidal drive is the major topic

of the paper.

Index Terms—Double stage cycloidal reducer,

epitrochoid, roulette.

I. INTRODUCTION

The modern application of a speed reducer requires

very large speed reduction along with high torque

transmission in small space. With conventional

gearing the trend is to increase load carrying capacity

by the use of high strength material. Higher accuracy

of the tooth profile, lubrication and cooling helps to

improve efficiency and performance. The

conventional gearing contains more number of power

transmitting components which leads to increase in the

inertial effects [1]. To overcome this limitation,

cycloidal speed reducer is used.

Cycloidal speed reducer finds its application in joint

of RV-3SB series of robots. The main reason being it’s

light in weight, have high transmission ratio, high

efficiency and good load carrying capacity. Most

importantly cycloidal speed reducer generated high

torque when compared to conventional gears [2]. In

order to design a cycloidal disc, one has to be familiar

with the forces acting on the disc. These forces are

computed from relative position of input and output

shafts. Force distribution among various parts of

cycloidal disc including the resultant force and angle

are evaluated and corresponding stresses are also

calculated. The effect of various design parameters

such as eccentricity of input shaft and radius of

housing rollers based on forces and stresses are studied

to obtain the optimum eccentricity and roller radius

[3].

The configuration of the HGT inherently allows for

the widest range of reduction ratio, i.e., from 50:1 to

6500:1, and exceptional torque density (torque to

weight/volume ratio). In combination with carefully

designed tooth profiles, the 2-stage cycloidal drive is

designed to provide high stiffness, low power loss,

nearly zero backlash and lost motion, and smooth and

quiet operation.[4] So designing a double stage

cycloidal drive is need of time for higher gear ratios.

II. AN ASSEMBLY OF CYCLOIDAL

REDUCER

There are Japanese and Chinese made cycloidal

reducer as shown in the figure 1. The one in the figure

only has single stage with one input shaft for the

cycloid gear. The input shaft which is connected to

rotor motor, eccentrically (with eccentricity ‘e’)

meshes with the eccentric cycloidal disk in its central

hole of diameter‘d’. The disk is mounted on ‘n’

number of rollers, one number more than that number

of cycloidal tooth (n-1) on disk. The disk has few holes

of diameter ‘d1’ symmetrical arranged within disk’s

centre hole and the cycloidal tooth such that d1 is equal

to sum of diameter of the pin diameter ‘d2’ on output

shaft and twice the eccentricity. The disk is mounted

using bearing on the shaft.

Some of the New Designed Prototypes are explained

below and most efficient and economical Prototype is



manufactured and further experimentation are carried

out.

Fig 1: Assembly diagram of cycloidal reducer

Wiz. 1. Output shaft, 2. Rolling element bearing, 3.

Housing, 4. Base, 5. Carrier pins, 6. Cycloid gear, 7.

Eccentric bearing, 8. Washer, 9. Needle tooth pin, 10.

Needle tooth sleeve, 11. Housing, 12. Hub, and 13. Input

shaft.

III. CYCLOIDAL DRIVE AS A HIGH

STRENGTH DEVICE

Spur gears do have 1 tooth to 3 teeth in mesh at a time.

Hence their teeth have to go through highly fluctuating

fatigue cycle when operating since load is shared by

the respective teeth. This gives rise to low life cycle of

spur gear and to increase the life cycle, more material

has to be added for more strength.*** Since power is

transmitted through multiple teeth engagement

harmonic gear drive offers high output torque capacity

than conventional planetary gear drive having nearly

twice its size and thrice its weight.

On the other hand cycloidal drives operate as a in cam

follower fashion and all the teeth are in mesh with

rollers hence force is separated over number of rollers

and in smoothly distributed fashion thus giving rise to

a sinusoidal fatigue distribution which is safer for

fatigue life cycle.

IV. MODELLING OF A CYCLOIDAL

DRIVE

The definition for an epicycloids is - a curve, produced

by tracing the path, generated by a chosen point of a

selected circle, called epicycle. This is rolling without

slipping around another fixed circle. Usually extended

epicycloids also called as epitrochoid are used for

generation of cycloidal drive.

The cycloid profile generation in CAD environment is

necessary for the manufacturing using modern

manufacturing techniques like, precise wire cutting,

CNC milling, etc. CAD modelling softwares like creo

parametric, Solidworks, etc possess platform for

tracing equations. And once equations are obtained for

profiles like cycloid, they can be easily modelled on

them.

Given a base curve, let another curve roll on it, and call

the point rigidly attached to this rolling curve the

"pole." The following table then summarizes some

roulettes for various common curves and poles. Note

that the cases curtate cycloid, cycloid, and prolate

cycloid are together called trochoids, and similarly for

the various varieties of epicycloids (called

epitrochoids) and hypocycloids (called

hypotrochoids).

Fig 2 a) shortened or curtate Epicycloid

Fig 2 b) extended or prolate Epicycloid

(Image-source: Wolfram Math-world)

The roulette[6] traced by a point attached to a circle of

radius rolling around the outside of a fixed circle of

radius . These curves were studied by Dürer (1525),

Desargues (1640), Huygens (1679), Leibniz, Newton

in 1686, L'Hospital in 1690, Jakob Bernoulli in 1690,

la Hire in 1694, Johann Bernoulli in 1695, Daniel

Bernoulli in 1725, and Euler in 1745 and 1781. An

epitrochoid appears in Dürer's work Instruction in

Measurement with Compasses and Straight Edge in



1525. He called epitrochoids spider lines because the

lines he used to construct the curves looked like a

spider.

The parametric equations for an epitrochoid are

V. MODELLING OF A TWO-STAGE

CYCLOIDAL DRIVE

A traditional design is made by the simple

combination of two single-stage cycloidal speed

reducers. The output shaft of the first stage is at the

same time input shaft of the second stage.

Taking into account that for each stage two identical

cycloid discs are used, rotated in respect to each other

by the angle of 180, in order to obtain uniform load

distribution, it means that the traditional two-stage

cycloidal reducer has four cycloid discs in total.

Fig.-3: The traditional design of a two-stage cycloidal

speed reducer

(1—input shaft with the eccentric (the first stage), 2—

the first stage cycloid discs, 3—stationary ring gear of

the first stage, 4—output disc of the first stage with

output rollers and output shaft, 5—input shaft with the

eccentric (the second stage), 6—the second stage

cycloid discs, 7—stationary ring gear of the second

stage, 8—output disc of the second stage with output

rollers and output shaft).

But this combination increases the axial thickness of

the gearbox and thus needs optimization.

VI. NEW DESIGN OF A DOUBLE STAGE

CYCLOIDAL DRIVE

Multi-staging is allows the design gearboxes for

higher ratios and in case of cycloidal gearboxes, lesser

mass and very higher gear ratio up to 600 is easily

achieved with least number of parts as compared to

rest of traditional gear boxes like spur, epi-cyclic, Etc.

Now newer design demand of lesser number of parts

and so just by increasing one disk and intermediate

shaft, I can achieve a double stage cycloidal drive. The

configuration of suggested design is achieved by

uniting output shaft of first stage and input shaft of

second stage into one intermediate shaft. It thus

allowed transmission of power between two stages.

Fig.-4: New design of a two-stage cycloidal speed

reducer

(4—in proposed design, modified intermediate link)

(Rest of the details as per Fig-3.)

We designed the suggested model for gear ratio 25.

We prototyped it in FDM and studied it. As expected

it gives 625: 1 gear reduction ratio. Some clearances

got induced because of the contraction of fused

deposition of ABS did not caused problem in its

working. The gearbox was not balanced and hence

vibrations were observed in the prototype. Next goal

will be to balance the drive and 2nd iteration using

FDM.

( )cos cos( ) )

( )sin sin( ) )

a bx a b t h tb

a by a b t h tb



VII. CONCLUSION

Its observed that The Dynamics of the Discs

equivalent will play a major role in vibrations of

Overall assembly. Balancing of the drive is as

important as the meshing of the gear drive since in

decides reliability of the product. There is a always a

creative scope in designing Two-stage cycloidal

reducers since they are not bound to specific

boundaries and optimisation is possible in radio holes

of cycloidal disk and overall thickness of assembly in

independent way.

AKNOWLEDGMENT

Especially thanks to the reference authors who helped

me get better understanding of the unique concept.

I thank my Head of Department Dr. K. B. Waghulde,

Our Dean Dr. R. V. Bhortake, our Principal, Dr. C. M.

Sedani, for motivating me to write a paper and their

motivation for Research.

I thank to Prof. G. V. Shah, for his motivation and for

his valuable suggestions.

REFERENCES

[ 1 ] Caetano Pacheco, (2011) Analysis of Cycloid

Drives Dynamic Behaviour, Retrieved January

20,2015.http://is.mfkg.kg.ac.rs/podaci/Mirko_

Blagojevic/63/M_Blagojevic_Analysis_of_Cy

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design of double stage cycloidal drive using roulette...

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