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full Paper - Nguyen Dang Binh

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ical velocities are estimated in about 1m/s for the maximum<br />

velocity, 1g for the maximum acceleration.<br />

All devices should be designed in order to show the lowest<br />

friction it is possible. The Maximum Friction parameter<br />

can be considered as indicative of the design quality. High<br />

friction values decrease the interface admittance resulting in<br />

a general degradation of the displayable-force resolution and<br />

in the increase of the force thresholds (force required to the<br />

contact for a movement).<br />

Small motors, direct-drive based design, low transmission<br />

ratios and simple design help to keep the global friction<br />

small.<br />

Coupling Effects generally arises when unwanted motions,<br />

principally due to static reaction forces and the kinematic<br />

arrangement of the haptic interface, alter the movement<br />

the user is trying to perform. This is particularly evident<br />

when the user is attempting to execute some kind of<br />

fine adjustment motions. Coupling may be static or dynamic,<br />

compensation techniques and feed-forward compensation of<br />

the manipulator dynamics help to keep down this parameter.<br />

All mechanical structures are subjected to deflections. The<br />

deflection, under static external disturbances is a function of<br />

the haptic interface compliance, the drive compliance, the<br />

servo system compliance and the transmission compliance.<br />

This sort of interface stiffness can degrade sensations when<br />

trying to simulate the contact/interaction with some “hard”<br />

(low admittance) virtual object. Haptic interface stiffness,<br />

cannot be measured or corrected by means of control software<br />

and consequently should be kept as low as the task and<br />

the interface scope require.<br />

When developing a system for a human operator, some<br />

maximum values for the minimum interface stiffness can be<br />

given. In fact, operator senses cannot distinguish between<br />

contacts with very “hard” objects (such as wood or steel)<br />

in terms of stiffness since the operator’s skeleton/tendons<br />

structure is much less stiffer than the objects. Consequently,<br />

depending on the kind of haptic interface, some maximum<br />

reference value can be established. These values can be furthermore<br />

reduced if in the virtual environment no such stiff<br />

object has to be reproduced.<br />

A rule of thumb for the minimum stiffness of the HI<br />

equals to the minimum between the human stiffness and the<br />

VE-objects maximum stiffness.<br />

The Inertia should be kept as low as possible for the interface<br />

design. Inertia lowers the admittance of the interface.<br />

Devices capable of high endpoint admittance provide the operator<br />

with more sensitivity at low force levels. During an<br />

experimental session two different kinds of inertia can be<br />

felt from the operator: the virtual-object inertia (which is<br />

programmed by the control law) and the interface inertia. In<br />

most common control schemes, the inertia loads are not canceled<br />

by the system. The suppression of the inertia factor by<br />

c­ The Eurographics Association 2005.<br />

Massimo Bergamasco / Haptic Interfaces<br />

5<br />

means of feedback control is truly hard. This operation required<br />

the information about the interface acceleration available<br />

into the environment. Since the interfaces generally provide<br />

data about position, acceleration can be only derived by<br />

means of double derivation which introduces noise and consequently<br />

errors in the computation. The detailed analysis on<br />

the influence of derivation errors on the inertia’s compensation<br />

was carried out by Adelstein in 1989. He concluded that<br />

a good compensation is not always feasible with the available<br />

control hardware for haptic interfaces.<br />

The inertia factor, the Gravitational Effects of the manipulator<br />

should be counterbalanced whenever it is possible.<br />

Even if it is feasible to provide control signal to cancel these<br />

effects with motors, this operation will require that motors<br />

operate with unbalanced load and therefore a powerful set<br />

of motors which should be able not only to reproduce the<br />

desired force at contact but also to cancel the additional gravity<br />

forces caused by mass umbalancing. Whenever a detailed<br />

design could improve the system balance, the overall performances<br />

improves since proper motors and transmission can<br />

be chosen for the system.<br />

A particular care should be given to the effective gain ratio<br />

to be adopted during the interface design. Higher ratios<br />

imply that the interface movements are largely reduced in<br />

comparison to the motor movements that caused them. Increasing<br />

such transmission ratio will help to improve the<br />

manipulator precision and to diminish the mass effect due<br />

to manipulator dynamic as seen on the motor shafts.<br />

As Townsend and Salisbury explained [12,13] increasing<br />

the overall gain ratio of the manipulator transmission does<br />

not produce positive effects on haptic interfaces. This can<br />

be seen if we imagine the haptic mechanics as a two-ports<br />

units which maps forces and positions the motor produces<br />

onto positions and forces the operator displays. In fact, in<br />

the case of an ideal manipulator (Zero mass, no friction, perfectly<br />

rigid links and joints with no compliance due to structure<br />

or transmission), the functional rules of this block can<br />

be expressed as:<br />

Mδω FδP<br />

where we imagined a simplified structure where all rotational<br />

motors produced a vector M of torques to which corresponds<br />

a vector δω of movements. The expression above<br />

represents the principle of “Virtual Work” for a non dissipative<br />

mechanism. When we apply a gain ratio between δω and<br />

δP such as δω KδP we obtain that F KM. Recalling that<br />

the mechanism is just a two ports device, the above relation<br />

states that improving accuracy in positioning of the motors<br />

and their maximum forces reduced at the haptic contact will<br />

cause a degeneration in the force and position sensitivity of<br />

the control.<br />

If we reconsider the effects due to friction, compliance

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