Detection of Mechanical Play of Revolute Robot Joint

Radim Luˇza and Frantiˇsek V. Zboˇril

Faculty of Information Technology, Brno University of Technology, Boˇztˇechova 2, Brno, Czech Republic

Keywords:

Play Detection, Revolute Joint, Robotic Manipulator, Mechanical Oscilator.

Abstract:

This article introduces a method of detection of mechanical play of revolute joint based on recognition of

impacts caused by the play. The method uses inexpensive acceleration measuring device with limited sampling

frequency. The impact is recognized indirecly according to oscillation of mechanical oscilator. The method

was tested on real servo drive Dynamixel AX-12A.

1 INTRODUCTION

In todays world robots equipped with manipulators

are rather widespread and they are becoming still

more casual. They are being used for tasks of many

different kinds. Precise control of the robotic manip-

ulator is essential for most of them. Controller of

robotic manipulator has to deal with kinematic and

dynamic properties and constraints of the manipula-

tor and payload it carries. A lot of effort was in-

vested into exploring areas of manipulator kinematics

and dynamics with rather impressive results. Today

there are software tools and simulators for simula-

tion of manipulators forward kinematics and forward

and backward dynamics like Gazebo (Koenig and

Howard, 2004) or Webots (Michel, 2004), libraries

of algorithms for solving inverse kinematics prob-

lem and planning trajectory of the motion for most of

kinds of manipulators like OMPL (S¸ucan et al., 2012)

and also tools that automate process of ﬁnding effec-

tive analytic inverse kinematics solvers for open kine-

matic chain manipulators (with some constraints) like

OpenRAVE (Diankov, 2010).

Often used way of controlling a robotic manipula-

tor is based on simulation. The controller has precise

model of manipulator it controls and before it moves

the real manipulator it ﬁnds and tests the motion with

the simulated one. Controllers of this kind are rather

robust and can be used with manipulators of many dif-

ferent kinds without need of changing their internal

structure. Especially if they use planners and solvers

based on iterative numerical algorithms.

Precision of controlers based on simulation is usu-

ally limited by conformity of model and real manip-

ulator. Basic kinematic parameters of the manipula-

tor - sizes of links, joint limits, link bounding objects

- are usually available as a part of production docu-

mentation of manipulator and these values are usually

precise. For measurement of manipulator dynamic

parameters there are several algorithms like (Gautier

M., Janot A., Vandanjon P.O., 2008) and others that

provide results usually with good precision. Theo-

retically identiﬁcation algorithms are limited only by

precision of used sensors - mostly encoders in joints

of robotic arm. Unfortunatelly precision of identiﬁ-

cation procedure aimed on obtaining parameters of

robotic arm manipulator is limited by properties of

the manipulator that are difﬁcult to identify. One of

them is mechanical play (backlash). Mechanical play

is difﬁcult to identify in general. Play can be hardly

detected by joint encoder beacuse its resolution is

usually limited. Identiﬁcation is especially difﬁcult

if manipulator has encoders installed on joint motors

instead of joint axis to increase resolution of position

measurement. Disadvantage of this solution is that the

mechanical play between gears of gearbox and play

of bearings can not be measured by encoder. Anyway

mechanicalplay is one of aspects that make difference

between real manipulator and identiﬁed model.

2 MECHANICAL PLAY OF

REVOLUTE JOINT

Most of robotic manipulators use at least one revo-

lute joint. Revolute joints have evolved from simple

joints with one degree of freedom (DOF) to two DOF

joints with differential drive or three DOF robotic

wrist (Meng Li, 2003). Play in revolte joints causes

327

Luža R. and Zboril F..

Detection of Mechanical Play of Revolute Robot Joint.

DOI: 10.5220/0005018203270332

In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2014), pages 327-332

ISBN: 978-989-758-040-6

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

imprecision of end effector positioning. The longer

the manipulator link is the more signiﬁcant the effect

of a play is. According to intallation of encoder there

are two solutions used in revolute joints: with encoder

connected with the motor and with encoder connected

with joint axis. In a typical construction of articulated

revolute joint the encoder is connected directly with

the motor. In this construction play of gearbox can not

be detected by encoder. This construction is modeled

by model described in (Ahmad, 1985). Mechanical

play in this model is given by gaps between teeth of

gears, by play of bearings and also by dynamic defor-

mation of gearbox. When motor of the joint starts to

move it has to overcome gap caused by play so part of

its motion is lost compared to output of encoder. This

effect is called lost motion (Ahmad, 1985).

Another construction of articulated revolute joint

typical for small servo drives uses high resolution

encoder or potentiometer connected with joint axis.

This solution is theoretically capable of detecting me-

chanical play of gearbox. If resolution of the encoder

is high enought it is possible to detect play of arm link

caused by gaps between gears by change of encoder

value. Practically the play would have to be bigger

than encoder step which can not be inﬁnite small. For

example in case of Dynamixel AX-12A servo drive

(Collective of employees of ROBOTIS ComSchool ef

Electrical Engineering, 2006) the encoder has 1024

steps per rotation which means that the lost motion

would have to be more then or equal to 21’ (angular

minutes). This value multiplied by length of link con-

nected to the joint gives us a length of an arc that end

of link can traverse without noticing by encoder.

2.1 Model of Play between Two Spur

Gears

Typically the most signiﬁcant source of play in rev-

olute robot joints are gaps between teeth of gears in

gearbox of the joint. Play caused by spur gears is

usually much bigger than play caused by bearings -

especially in case of inexpensive servo drives. For

this reason we decided to simplify model of play to

model play caused by spur gears only. Model of force

transmission between gears we use was presented in

(R. Kalantari, 2009). For each pair of spur gears the

model of contact force is following:

cnt

= F

+ F

= β ·



∆d

d/2



+ α·∆v ·



∆d

d/2



n+1

(1)

In equation 1 the F

member is an elastic force

and the F

is a viscous force. The ∆v is a difference

of linear speed of gears at the point of contact, the ∆d

is a difference between linear positions of spur gears

at the point of contact and the α and β coeﬁcients are

special constants that convertforces to proper size and

unit. The exponent n is a large odd number.

In the model of spur gears the ﬁrst gear is actuated

by ideal actuator with no inertia, no backlash and inﬁ-

nite torque. This actuator changes position of the ﬁrst

gear with index 1. The second gears with index 2 is

is actuated by the ﬁrst gears through teeth with back-

lash. Force between teeth is described by equation 1.

The F

cnt

force causes angular acceleration of the sec-

ond gear. The angular acceleration is given by inertia

of the second gear and its radius R

according to

equation 2.

′

= −

cnt

. (2)

Change of position of particular tooth on each gear

is given by corresponding relation in 3 where θ de-

notes angular position of particular gear.

= θ

·R

; p

= θ

·R

(3)

The shift between teeth of gears required for com-

putation of the contact force F

cnt

is described by equa-

tion 4. The difference between linear speeds of teeth

at the point of contact of the gears is given by equation

5 in a similar way.

∆d = p

− p

(4)

∆v = p

′

− p

′

(5)

Response of the model of spur gears with play can

be observed in ﬁgure 1. As input signal for the model

the sine signal at frequency 6 Hz was used. The input

signal controls angular position θ

of the ﬁrst gear.

It is a simpliﬁcation that we can use thanks to ideal

actuator with inﬁnite torque so inertia of the ﬁrst gear

has no effect and we can neglect it.

In the ﬁgure we can see that the gaps between

teeth cause visible peak in angular acceleration of

the second gear. The peak in acceleration practically

means that the contact of gears that are spinning each

with different angular speed cause impact.

2.2 Current Methods of Measuring and

Compensation of Mechanical Play

Currently the most of effort is aimed on elimination

of the play itself. Elimination of mechanical play

includes sophisticated design of gearbox and a very

precise manufacturing of manipulator parts. Elimi-

nating the play is absolutely the best solution. Unfor-

tunatelly this solution is very expensive. It is usable

for industrial manipulators which save a lot of money

by doing mechanical work effectivelyand their higher

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics

328

Figure 1: Response of spur gear model with backlash to sine

excitation.

initial price is not a problem. But in case of experi-

mental and prototype manipulators a high initial price

is a serious problem. Experimental manipulators are

usually built of inexpensiveserial parts. They are usu-

ally equipped with common bearings and inexpensive

joint drives. With such a low cost construction it is

usually difﬁcult to avoid mechanical play. Moreover

there is also higher probability of quick wear out or

mechanical damage of the manipulator. In case of

low-cost experimental manipulators it is useful to be

able to detect and measure mechanical play.

Measuring and compensation of mechanical play

is described in (Ahmad, 1985) and (Hyun-Kyu Lim

and Kang, 2009). In (Ahmad, 1985) imprecision of

manipulator caused by several aspecs including play

is compensated according to feedback of human op-

erator who measures total error of manipulator end-

point. The paper also presents procedure leading to

excitation of mechanical play. The effect of play is

mechanical overshoot of desired arm endpoint posi-

tion. The overshoot can be converted into angular

displacement of revolute joint and according to this

displacement the compensating shift in motor angle

is computed. To compensate properly the manipula-

tor controller needs to keep a direction of previous

motion to decide whether mechanical limit given by

play was reached and which one.

In (Hyun-Kyu Lim and Kang, 2009) authors de-

scribe a method of measuring and compensation of

mechanical play for industrial manipulator Hyundai

HS165. The described method iteratively changes

compensation parameters to minimize error between

computed endpoint position and measured endpoint

position. The paper also describes extention of the

original method to include compensation of errors

caused by stiffness of manipulator parts.

Both methods described abovewere developed for

stationary industrial manipulators. They provide very

precise compensation of errors caused by play and

other aspects but they both require very precise mea-

surement of end effector error. The measurement is

done by measuring by hand (Ahmad, 1985) or by ex-

ternal sensors (Hyun-Kyu Lim and Kang, 2009). Un-

fortunatellyprecise external measurement of endpoint

position is usually rather difﬁcult and expensive to re-

alize. Measuring device has to be installed and pre-

cisely calibrated in relation to basepoint of the ma-

nipulator. It may cause difﬁculties especially in case

of mobile robots where is usually not much space for

proper installation of sensors measuring endpoint po-

sition. In this paper there is proposed an inexpensive

and rather easy to establish method for detecting me-

chanical play based on impact detection.

3 DETECTION OF

MECHANICAL PLAY

In the method proposed below the mechanical play

is detected indirectly by detecting impacts caused by

mechanical play between two moving spur gears in

a gearbox. If there were no gaps between teeth of

gears in the gearbox the input motion would be trans-

ferred to the output affected only by gear ratio. It

means that the output trajectory would have the same

shape as input one. If acceleration of the excitation

motion is sine wave the output of the ideal gearbox

would be also perfect sine wave. In real situation

small gaps between teeth deform output acceleration

trajectory as can be seen in ﬁgure 1. The peeks in

acceleration caused by impact when teeth of the ﬁrst

gear meet the theeth of the second gear are easy to

recognize in simulation but in real measurement it is

not that easy to recognize them. The real measure-

ment contains a lot of noise. The noise also contains

peeks that can easily interfere with peeks caused by

play so detection of play based on detection of peeks

in acceleration would detect many false alarms. The

solution we decided to use also uses the impact peeks

but not directly. In proposed solution acceleration

peeks shake a mechanical oscilator that starts to os-

cilate. The periodic oscilation of the known oscilator

is then much easier to detect.

To model output of the oscilator we used standard

model of damped oscillation described by equation

6. The model is based on principle of preservation of

energy in isolated system. The m coeﬁcient denotes a

generalized mass, b is a breaking coeﬁcient that is re-

sponsible for decreasing of amplitude in time, the k is

a spring elasticity coeﬁcient and the q is a generalized

coordinate.

m·q

′′

+ b·q

′

+ k·q = 0 (6)

This model was interconnected with model of spur

gears with mechanical play described in prior section.

The interconnection was done by adding acceleration

DetectionofMechanicalPlayofRevoluteRobotJoint

329

Figure 2: Position of free end of the mechanical oscilator.

caused by motion of the second gear to the accelera-

tion in the equation 6. The oscilator is installed on a

metalic bar connected with one end to the axis of the

second spur gear in a direction orthogonal to the axis.

The lenght of the bar is l and the ω

coeﬁcient is an-

gular acceleration of the second spur gear. Equation

7 describes extended damped oscillation model. Ac-

celeration of the oscilator connected to the spur gear

model with the same conditions that were used in pre-

vious section can be observed in ﬁgure 2.

m·(q

′′

+ ω

′

·l) + b·q

′

+ k·q = 0 (7)

In ﬁgure 2 appear small periodic waves in a sine

trajectory of acceleration. These waves are caused by

resonation of the oscilator.

Of course the oscillation of the oscilator causing

fast small periodic change in acceleration mix with

acceleration changes caused by motion of the second

spur gear and with noise but it can be detected in spec-

trum. In spectrum it is possible to to ﬁlter out only the

particular frequency - the resonation frequency of the

oscilator - and omit all other frequencies. In spectrum

the presence of oscillation of the oscilator can be de-

tected by amplitude of the resonation frequency of the

oscilator. Despite the theory that tells us that we can

ﬁlter out only one particular frequency in real solu-

tion we have to ﬁlter out a small range of frequencies

because due to dumping and some parts that shake in

moment of impact the oscillation of the mechanical

oscilator is not perfect. Processing of input signal is

described by following equation. Output of the equa-

tion is a scalar value o that we can compare to some

level value. If o is greater than level value impact is

detected.

o =

∑



norm( f ft(~s

), f

norm

, f

norm

)

mask



(8)

Where ~s

is a vector of measured values,

mask is a

mask vector of ones and zeros and norm is a nor-

malization function that will be decribed later. When

spectrum of input signal computed by fast Fourier

transform from input vector is multiplied element by

element by mask vector, only subsequence of spec-

trum is ”selected” and the rest of elements of spec-

trum vector change to zero in result. Note that

de-

notes a Hadamard (elementwise) product of vectors.

There are three parameters that can change be-

haviour of the method and setting their proper val-

ues is essential to reach good reliability. The ﬁrst

two parameters describe ﬁlter that extracts informa-

tion about impact from the spectrum according to

equation (10). These are frequency of resonation of

measurement equipment f

res

and width of detection

window f

width

. Effect of f

res

is rather straightforward.

The window width f

width

on one hand should be wide

enought to not to miss the peak that can become rather

wide in real signals because of imperfect oscillation

as desribed above but on the other hand it can not

be too wide to receive noise. Third parameter that

has signiﬁcant impact on results of this method is the

level value mentioned above that o

scalar

is compared

to. This level value has the same effect as detection

levels in classiﬁcators. The level needs to be tuned to

obtain the best ratio of proper detection to false pos-

itives and false negatives. The optimisation equation

for level value is following:

level =

= argmax



correct

accept(eval( f

res

, f

width

,ss,x))

false positive(eval( f

res

, f

width

,ss,x))

correct

reject(eval( f

res

, f

width

,ss,x))

false negative(eval( f

res

, f

width

,ss,x))



(9)

Function eval(X,Y, Z) is a funtion that evaluates

runs of the method described above. It runs with

sample set ss and with constant properly set param-

eters f

res

and f

width

and level x which is object of

optimisation. The function returns a matrix of re-

sult values of correctly accepted samples (play de-

tected), correctly rejected samples (play not detected)

and false positive and false negative detections. Func-

tions correct

accept, false positive and others are

functionsthat return value they describe by their name

from the result matrix.

The

mask vector compounds of mask

compo-

nents. According to resonation frequency of oscila-

tor f

res

and width of detection range f

width

each co-

eﬁcient of masking vector is computed. The com-

putation is deﬁned by following equation. Function

freq

f ft converts real frequency to coeﬁcients of fast

Fourier transform

The function freq

f ft in equation (10) would require

also sampling frequency and cardinality of input vector as

arguments but for better readability of the equation these

parameters were omitted.

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330

Figure 3: Block diagram of entire solution.

mask







1,i ∈< freq

f ft(f

res

− f

width

/2)),

freq f ft(f

res

+ f

width

/2)) >

0,otherwise

(10)

Function norm is normalization function. This

function normalizes each sample of spectrum by nor-

malization coeﬁcient. Normalization coeﬁcient is

computed as average of subsequence of amplitude

values extracted from spectrum. The f

norm

argument

deﬁnes frequency which will be the center of subse-

quence extracted from vector of spectrum. Length of

the sequence is deﬁned by f

norm

. Average of the ex-

tracted sequence is used as normalization value that

divides each element of spectrum vector. Function

norm returns vector of normalized valuesof spectrum.

Complete solution can be observed in ﬁgure 3.

As a mechanical oscilator can be theoretically

used any object that will resonate after impact. Theo-

retically the manipulator links themself could be used

as oscilators but practically there are some shortcom-

ings. Usually the robotic manipulator links are robust

and have complicated shape. Due to it manipulator

links have usually very high and hardly predictable

resonation frequency and its resonation is quickly at-

tenuated so detector of oscillation would have to be

extremly sensitive. The sensitivity of the detector

brings a serious problem with noise. This can be

solved by using properly formed metal bar as the os-

cilator. We used a metal bar installed on manipulator

link in direction parallel to direction of manipulator

link - one end is ﬁxed on the manipulator link and

the other free end connected with acceleration sensor.

When impact occurs the metal bar starts to oscilate

like if it was hit by gavel. This way it is possible

to capture oscillation of metal bar when impact oc-

curs in joint of manipulator. Moreover we can change

resonation frequency and intensity of oscillation by

changing shape of the metal bar.

5000

10000

15000

20000

0 1000 2000 3000 4000 5000 6000

Amplitude

Fast Fourier Transform coeficients

Figure 4: Spectrum of acceleration during motion without

impact.

5000

10000

15000

20000

0 1000 2000 3000 4000 5000 6000

Amplitude

Fast Fourier Transform coeficients

Figure 5: Spectrum of acceleration during motion with im-

pact.

4 EXPERIMENTS AND RESULTS

Initial experiments were done on special experimen-

tal apparatus that is from mechanical point of view

very similar to metal bar with one end ﬁxed to revo-

lute joint and the other end free. To simulate play the

metal bar could rotate between two blocks that limit

its revolute motion - one ﬁxed and the other conﬁg-

urable. The entire apparatus rotates about the same

axis as the metal bar inside it does. This apparatus

was useful to prove the concept proposed in prior sec-

tion but its mechanical concept is still rather different

from real joint and links of manipulator. The appa-

ratus demonstrates change in the spectrum when play

appears as is visualized in ﬁgures 4 (without play) and

5 (with play).

To prove correctness of principle of the method

it was necessary to execute experiments on a real

robotic joint. A simple robot compounding of two

links connected together by AX-12 revolute servo

drive was used as experimental device. One link was

a ﬁxed base link and the other was free link. On the

free link there was installed measuring device - metal

bar with acceleration sensor. One end of metal bar

was mounted on the free link and the other end with

acceleration sensor was free.

The servo drive has a small play. During the test-

DetectionofMechanicalPlayofRevoluteRobotJoint

331

Table 1: Results of experimenting with real revolute joint

AX-12 servo drive.

Play True pos. [%] False neg. [%]

With play 98 2

W/o play 100 0

ing it was necessary to obtain also samples without

play. To ensure that the conditions for the measure-

ment of motion with play and without play will be

the same a small trick was used. The servo drive was

not used as a motivator. Base link of the experimen-

tal robot was actuated so entire experimental robot

was moving. To test detection of mechanical play the

robot was straightened and the servo drive was conﬁg-

ured to keep its position. The entire robot was waved

in direction perpendicular to the axis of servo drive

and to the common axis of both links so mechanical

play of the servo drive was excited. To test motion

without mechanical play the servo drive was bypassed

by mounting two links of robot together by solid met-

alic part so the servo drive could not move anymore.

Other difﬁculty was the actuator itself. It was nec-

essary to actuate entire robot by actuator without its

own play. As a simple solution of actuator without

play human hand was used. Human hand can hardly

generate perfectly periodic motion but for this exper-

iment it was not essential because impacts appear ev-

ery time the acceleration changes its direction.

Results of the experiment are shown in table 1.

The true positivein the table 1 means that the property

was detected correctly. The false negative means that

the property was not detected despite it was present in

the sample. False positive is not present in the table

beacause the properties are in mutual exclusive rela-

tion so false negative of one property is false positive

of the other.

5 CONCLUSION

In this paper a method of detection of mechanical

play based on impact recognition was proposed. The

method in proposed form is usable for revolute joints

only. Theoretical principles were tested on real joint

based on Dynamixel AX-12A servo drive. Experi-

ments prove that the method is usable for distinguish-

ing between motion of servo drive with play and with-

out play. Reliability of detection was not perfect.

There are still several problems that need to be

solved in the future before the method will be us-

able in common use cases. Extending this method to

robots with more than one degree of freedom bring

a problem of distiguishing between sources of the

play - especially if there are two joints with parallel

axes. Another problem is automatized way of ﬁnd-

ing proper values for the parameters of the method

and also proper value of acceleration of the excita-

tion motion. It would be also very useful to extend

the method to not only detect the mechanical play but

also measure the size of mechanical play.

ACKNOWLEDGEMENTS

This work was supported by the European Regional

Development Fund in the IT4Innovations Centre of

Excellence project (CZ.1.05/1.1.00/02.0070).

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