Simulation of a manual gearshift

with a 2 DOF force-feedback joystick

Antonio Frisoli Carlo A. Avizzano Massimo Bergamasco

PERCRO

Scuola Superiore S. Anna

Pisa, Italy 56127

antony@sssup.it, carlo@sssup.it, bergamasco@sssup.it

Abstract

A 2 dof force-feedback joystick was employed to sim-

ulate the force response of a manual gearshift of car

during drive. The control law is based on an hybrid

model. A state machine determines the active state of

the system, according to the simulation, and changes

the parameters of the dynamical model. The operator

can move the gearshift lever whether such a movement

would be allowed in an actual transmission under simi-

lar circumstances. The obtained performance was com-

pared to the experimental data, measured on a real car.

The simulated and experimental results match satisfac-

torily and the joystick gives a realistic feel of an actual

manual transmission.

1 IntroductionVehicle simulators, and in particular aircraft simu-

lators for use in training pilots, can be equipped with

various control devices such as acceleration, brake and

clutch pedals, gear change lever and steering wheel, to

enhance the realism of the simulation.

The adoption of Haptic Interfaces (HI) inside simu-

lator systems appears to be an added value, improving

their functionality. HI allow to logically program and

control their mechanical response. In such a way in

tests inside simulators users can evaluate the vehicle by

changing either kinesthetics or haptic parameters. This

is particularly useful when ergonomics aspects are taken

into consideration [1, 6].

In most of simulators [7, 2, 5], control commands

are employed as passive sensorized systems, replicating

the interaction forces exchanged during normal drive

conditions.

In [8] the steer wheel was replaced with a force con-

trolled Haptic Interface, whose behavior was based on

an internal numerical model of the vehicle.

The ATARI corporations patented two inventions re-

garding the simulation of a gearshift [3, 4]. The de-

vised systems are based on a mechanism allowing the

gearshift lever to pivot around at least two axes. In

the �rst invention [3] the mechanism is equipped with

electrically operable clutches, that can cause only resis-

tance to the movement of the lever. Positional sensors

and strain gauges coupled to the gearshift lever sense

the lever movements and forces.

In the second invention [4] a solenoid is coupled to the

pivoting mechanism to control the amount of applied

force.

This paper presents the design of the control law for

an HI, to be integrated as a gear change lever in a car

driving simulator, aimed at evaluating the ergonomics

of internals of car in Virtual Environments [1]. A com-

mercially available force feedback joystick was used to

assess the control algorithm. The control law will be

�nally implemented on a 2 DOF Haptic Interface pro-

totype, currently under construction at PERCRO.

The paper is organized as follows. The second section

brie y introduces the mechanical working principles of

a manual transmission gearshift. Section three explains

and discusses the analytical model of a single gear en-

gagement and compares the experimental results, mea-

sured on a real car, to the simulated ones. Finally sec-

tion four presents the control law of a complete manual

gearshift.

2 Mechanical description of a manual

transmission gearshiftThe gearshift changes the gear ratio between the pri-

mary shaft, connected by the clutch to the motor, and

the secondary shaft, conversely permanently connected

to the di�erential unit and so to the wheels shaft. In fur-

ther considerations the clutch pedal is always assumed

pushed to the oor.

In a manual transmission the driver can move the

gearshift lever transversally to select and longitudinally

to engage the gear. Later on we will call these direc-

tions respectively y and x, as illustrated in �gure 1. An

external command system connects the gearshift lever

to the gear-box, generally placed in the front part of

the car.

The external command converts the movements of

the gearshift lever in movements of a coupling in the

Figure 1: The gear positions as seen from the driver

seat

gear-box. It is implemented with di�erent mechanical

solutions, but the main ones are exible (single or dou-

ble Bowden), rigid (connecting and push rods) or hy-

brid. The adopted solution in uences the compliance

of the overall system as perceived by the driver.

The couplings in the gear-box are generally sliding

keyed to either the primary or the secondary shaft. For

instance we can suppose that the coupling is keyed to

the secondary shaft (this is commonly the case of the

coupling that engages the �rst and the second gear).

As shown in �gure 2 two gears are keyed with the pri-

mary shaft, permanently in mesh with two correspond-

ing gears idle on the secondary shaft. The coupling

can engage one of the idle gears on the secondary shaft,

with a sliding motion along the shaft (corresponding

to an x movement of the knob), and so create the mo-

tion transmission between the primary and secondary

shafts. Since the idle gears are driven by the primary

shaft, before the mesh occurs, there is a relative angu-

lar movement between the idle gear and the coupling.

For achieving a quiet and smooth engagement, the two

gears to be engaged must be brought to approximately

the same angular velocity. This is realized by an in-

termediate synchronizing gear in two stages: the pre-

synchronization and the synchronization. Only after

the synchronizing stage the full engagement takes place.

2.1 The three stages of the gear engage-ment

The three di�erent main stages, occurring during the

gear engagement, characterize the particular force re-

sponse of a gear-shift: the synchronization, the engage-

ment and the impact against the mechanical stop. Since

the gearshift is a multi-body dynamical system, each

stage is associated to the interaction of di�erent parts

in the gear-box. In the following it is brie y explained

how the forces generated during the engagement are as-

sociated to di�erent stages.

Figure 2: Gearshift arrangement.

As shown in �gure 2, a ball-spring system (placed

in the housing of the lever mechanism) constrains the

lever in the selected gear position. So an initial pre-

set load must be applied to displace the lever from its

equilibrium position.

After the lever is released, another preset load must

be applied to displace the coupling from its neutral posi-

tion. In fact the coupling is hold in the neutral position

by a second ball-spring mechanism (placed in the gear-

box), whose function is to accomplish a softer mesh

between the synchronizing gear and the coupling. This

is the pre-synchronizing stage.

After the pre-synchronizing stage is achieved, the

synchronization can begin. The coupling, in mesh with

the synchronizing gear, pushes it against the idle gear.

The internal conical surface of the synchronizing gear

is brought in contact with the external conical surface

of the idle gear, which is rotating dragged by the pri-

mary shaft. The tangential friction forces, exchanged

by the two bodies in reason of their relative motion,

are so transformed in an axial force, through the taper

of the synchronizing gear. This axial force impedes a

further sliding motion of the coupling.

Until a relative motion between the synchronizing

gear and the idle gear exists, the coupling (and so the

gearshift lever) is blocked into a �xed position and can

not go forward. Only when the relative velocity be-

comes null, the \synchro gate" opens and the coupling

can continue its sliding motion.

At the end of synchronization, the coupling teeth of

the synchronizing gear and the idle gear come into col-

lision and �nally mesh. The impact force, generated by

the coupling tooth contact is random, since it depends

on the relative position of the teeth at the moment of

the engagement. After the full engagement, the lever

reaches a mechanical stop, based on a ball-spring sys-

tem also, and it stopped.

Figures 3 and 4 display data collected by sensorizing

the gearshift knob aboard an experimental car. Both

plots reveal typical force characteristics with respect to

time and engagement position.

10.6 10.7 10.8 10.9 11 11.1 11.2 11.3 11.4 11.5

0

1

2

3

4

5

6

7

8

Force during 1st gear engagement

time (sec)

For

ce (

Kg)

, pos

ition

(cm

)

force position

synchronizing

engagement peak

stop impact

position

force

Figure 3: Force and position vs. time, as measured

at the knob during neutral-�rst gear shift (courtesy of

CRF)

−10 0 10 20 30 40 50 60 70 80 90−2

0

2

4

6

8

10

Position (mm)

forc

e (k

g)

Force−position closed−loop diagram

Stop impact

Engagement

Synchronizing

Figure 4: Force vs. position, as measured at the knob

during neutral-�rst gear shift (courtesy of CRF)

The pre-synchronizing stage generates a negligible

force peak only and can be reasonably disregarded.

During the synchronization, both force and position

are held constant for a de�nite period of time, as shown

in �gure 3 and the force reaches its maximum value.

The engagement stage is characterized by an isolated

peak force, that generally is lower than the synchroniz-

ing force peak. Moreover the magnitude of such pick

force is not constant and varies remarkably at every

gearshift manoeuvre. During the engagement the posi-

tion remains also constant for a short time, as can be

revealed by data measured directly at the gear-box.

As shown in �gure 4 the synchronization and the

engagement peaks occur at de�nite x values. The

recorded data aboard the experimental car show a syn-

chronization peak at about 8 Kg that lasts 0.3 msec.

The engagement peak is instead instantaneous, since it

is due to the impact of the gears teeth. This double

bump of force, typical of the engagement process, gives

the user the usual feel of engaging the gear.

The �nal stage gives raise to the stop impact peak.

Since the lever is arrested by an elastic stop system

through the external command, the lever position has

an overshoot and a following recovery to the equilibrium

point, as shown in �gure 3.

The driver, changing into a gear, exerts forces on the

lever, determined mainly by the synchronization, the

engagement and the �nal impact with the stop. There-

fore a realistic simulation of a gearshift must replicate

these three phases.

3 The model of the gearshift engage-

mentAn analytical model of the gearshift behavior was

investigated to replicate a correct force-feedback to the

operator. From the analysis of the experimental data,

we chose to model the di�erent phases of the gearshift

adopting a dynamic model with both continuous and

discrete states (each discrete state was associated to a

gearshift stage). The gearshift response, representing

an hybrid model in itself, was developed as a MATLAB

Simulink/State ow module.

The GEARSHIFT ENGAGEMENT model, shown

in �gure 5, takes as input the user forces exerted on

the knob and provides as output the knob position and

velocity. The model can be divided in two parts:

1. A time varying continuous dynamics which de-

pends on the gear stage (GEARSHIFT DYNAM-

ICS).

2. A discrete state machine (GEARSHIFT STATE-

FLOW) which determines the gear stage on the

basis of the knob position and user' s force.

The GEARSHIFT DYNAMICS was implemented as

a parametric mechanical system composed of a massm,

spring k, damper c with a stick-slip friction:

Fdr = m �x+ c _x s+ k(x� x0) + Ffr (1)

GEARSHIFT ENGAGEMENT model

position

OUTPUT2

velocity

OUTPUT1

Force

INPUT

x

force

gs_stage

GEARSHIFT STATEFLOW

GEARSHIFT DYNAMICS

Driver force

GS_stage

X Position

Figure 5: The GEARSHIFT ENGAGEMENT model.

where Fdr is the driver force, x the position and the

friction force Ffr is given by:

Ffr =

8<:

Fdr if Fdr � c _x� k(x� x0) <= Fst

and _x = 0

else Fsl

(2)

with Fst and Fsl respectively the static and dynamic

friction coeÆcients. The parameters m; k; c; x0; Fst; Fsl

are set to di�erent values for each stage by the

GEARSHIFT STATE-FLOW module.

The GEARSHIFT STATE-FLOW module receives

as inputs the x position of the knob and the force ex-

erted by the user. The discrete states of the module

represent the di�erent gearshift stages outlined in pre-

vious section, i.e. the synchronization, the engagement

and the end impact. Moreover free motions states were

added to model the lever behavior out of these stages.

The input information are used to manage the tran-

sitions among di�erent states. For instance if the user

is pushing forward during the synchronization state, a

transition is activated to reach the engagement state.

Conversely if the force is suddenly reverted, a transi-

tion to a free motion state is activated.

The conditions under which the transitions can occur

are based not only on position and force, but on time

also. So the duration of the synchronization stage is

imposed by a time-dependent out-transition.

Actions and events broadcasting are associated both

to the transitions and to the states. In particular several

assignments to logical variables are executed according

to the active state. The logical variables, containing the

information about the active state, are then output to

the GEARSHIFT DYNAMICS module, which controls

the current values of the simulation parameters.

3.1 Simulation of the model

To test the eÆciency of such a model, a driver module

was also implemented in the Simulink environment.

The driver was modeled assuming that his force be-

havior is linear, inversely related to the gearshift knob

velocity by the law:

F = Fmax(1�_x

Vo

) (3)

where Vo is the target velocity and it is assumed equal

to the maximum one measured during the engagement

movement, while Fmax corresponds to the maximum

force that the user can apply. Such a force model of the

driver can be adapted to �t the behavior of di�erent

drivers.

The driver module was then interfaced to the

GEARSHIFT ENGAGEMENT module in a velocity

closed-loop (the position output of the GEARSHIFT

ENGAGEMENT module was not used in this simula-

tion).

Figure 6 shows the numerical results achieved during

the simulation. All main stages of the engagement are

replicated by the model. Model parameters were regu-

lated in order to match the maximum values of forces,

the positions and the reference times to the experimen-

tal results.

10.6 10.7 10.8 10.9 11 11.10

1

2

3

4

5

6

7

8

time (sec)

forc

e (k

g), p

ositi

on (

cm)

Force and position output of numerical simulation

force position

synchronizing

engagement force

position

impact force

Figure 6: Force and position vs. time output by the

numerical simulation

3.2 Experimental validation

A 2 dof force feedback joystick was employed for car-

rying out an experimental validation of the engagement

model. For such a purpose we used the \Wingman

Force Feedback Joystick" by Logitech, a commercially

available device with proper drivers and control board.

The Joystick is equipped with two DC motors and

two analog potentiometers, which are connected to the

handle through a 2 DOF parallel pivoting mechanism.

Such a mechanism allows the lever to pivot around

two co-planar axes. The motors transmit the torque

through a capstan tendon transmission system, which

increases the motor torques and reduces the backlash

between motors and potentiometers.

Since our aim was to test the eÆciency of the control

algorithm, we excluded the built-in control processor,

and connected the Joystick to a DSP DS1102 dSPACE

board. By a rough estimation we found that with the

DSP arrangement the maximum executable force at the

knob was about 10 N, that was one tenth of the target

force of 10 Kg we needed to replicate in the application.

Also the workspace dimensions were smaller than the

required ones. In order to assess the control algorithm,

the simulated results were scaled to the experimental

ones of �gures 3. We expect that the control law will

work �ne also on the PERCRO prototype, which was

dimensioned according to the force speci�cations.

We interfaced the Joystick to the Matlab environ-

ments through the Real Time Workshop toolbox. The

model was downloaded and run directly on the DSP

board. A GUI interface panel was developed to control

and capture the data from the simulation.

All simulations were performed at a frequency of 1

KHz to avoid problems related to simulation sampling

time.

An internal position servo-loop was used for con-

trolling the joystick position and providing interaction

forces to the gearshift model (see �gure 7). During sim-

ulation the y position of the joystick was set to zero to

simulate a 1 DOF sliding constrain.

0

Y_DES

PID

PID In_Fx

In_Fy

Out_x

Out_y

Joystick

FORCEX_DES

GEARSHIFT MODEL

DRIVER FORCE FY

Y_REAL

POSITIONERROR

DRIVER FORCE FX

DRIVER FORCE FX

X_DESIRED

Figure 7: The control of a single axis

The following plots show the obtained results. The

error on the force signal was determined by the electric

noise produced by the analog potentiometers. The sig-

nal noise did not allow to reduce more the duration of

the engagement.

Plot 8 shows the �ltered (with a low pass Butter-

worth �lter and a cut-o� frequency of 20 Hz) and the

non-�ltered force signal. The curve matches satisfacto-

rily the experimental one. The feeling during the en-

gagement was realistic, resembling a slow gear engage-

ment during drive. Although the hardware restrictions

did not allow to improve more the performance of the

system, the devised control law seemed to work prop-

erly.

6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 7.80

1

2

3

4

5

6

7

8

9

time (sec)

forc

e (k

g), p

ositi

on (

cm)

Force vs. time (filtered and unfiltered signal)

synchronizing

engagement

stop impact

POSITION

FORCE

Figure 8: Force signal estimated from the position error

−2 0 2 4 6 8

−6

−4

−2

0

2

4

6

8

10

position (cm)

forc

e (k

g)

Force−position closed−loop diagram

synchronization engagement end

impact

Figure 9: Force vs. position loop diagram during

neutral-1st gear shift

4 The complete gearshift modelAfter the simulation of a single gear engagement, we

stepped to the development of a complete gearshift (see

�gure 10).

The model was extended to consider the constrains

imposed by the slides of each gear. The y axis was con-

trolled by a parametric module with a lower number of

states, with respect to the x axis module. In particular

the workspace of the gearshift was divided, according to

the x and y, into numerous areas, associated to a dif-

ferent state of the gearshift. A main state- ow module,

called STATE-FLOW MANAGER, identi�es the cur-

rent area, and outputs this information to the X and Y

controller modules. Inside these modules, the users' s

action, either selecting transversally a gear or engaging

longitudinally a gear, is recognized, and the correspond-

ing state behavior is activated. Clearly when the user

is engaging a gear, the GEARSHIFT ENGAGEMENT

model of a single gear is activated to control the x posi-

tion. The slides constrains were replicated as mechani-

cal impedances, which restrain the knob into rectilinear

trajectories.

X POSITION

TO THE USER

FROM THE POTENTIOMETERSy

elez

ione

Fy

Y CONTROLLER

sele

zion

e x

Fx

X CONTROLLER

y x

ST

AT

ESTATEFLOW

MANAGER

In_F

y

In_F

x

OUTPUT

Out

_y

Out

_xINPUT

STATE INFO

FORCE X FORCE Y

Y POSITION

Figure 10: The complete model of the gearshift

The simulated workspace is shown in �gure 11.

−8 −6 −4 −2 0 2 4 6 8−10

−8

−6

−4

−2

0

2

4

6

8

10

Y axis (cm)

X a

xis

(cm

)

Workspace

1

2

3

5

4

Figure 11: The simulated workspace (scaled)

5 Future DevelopmentsAn Haptic Interface (HI) dedicated to the gearshift

simulation is currently under construction at PERCRO

laboratory. The control problems depending on the

hardware restrictions will be overcome with such a new

device. In fact the HI will be equipped with high resolu-

tion optical encoders and DC iron-less motors capable

of exerting to the knob forces up to 20Kg. Moreover

the workspace will be conformal to the requirements of

the application and the mechanical bandwidth greatly

enhanced. The results of the present work will be uti-

lized to control the HI.

6 ConclusionsThe present paper describes a control law of an HI

for a manual gearshift simulation. The control law is

based on an hybrid model, with both continuous and

discrete states. The performance of the control law was

preliminary estimated on a 2 DOF force-feedback joy-

stick, with satisfactory results.

7 AcknowledgementsThe authors are grateful to CRF (Centro Ricerche

FIAT) for the provided technical support. This research

was supported by European Commission \GROWTH"

Programme Research Project \Virtual" (Virtual real-

ity systems for perceived ergonomic quality testing of

driving task and design) under contract nr. 1999-

RD.11030.

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