Kinematic and dynamic analysis of a sit-ski to improve vibrational comfort

Introduction

The number of users of winter sports equipment hasincreased in recent last years. Many new disciplinessuch as snowboarding, freestyle, eliski have grown.

Among these different ways to practise skiing, ‘sit-ski’has attracted special attention, not only as a new wayof skiing, but, above all, for the possibility opened todisabled people to practise winter sports. ‘Sit-ski’ is anacronym for skiing in a sitting position and identifiesthe tool which makes it possible. A sit-ski is normallymade of light alloys, similar to those used for bicycleframes (magnesium, titanium, aluminium up tocomposite materials), and is essentially composed ofthe following four parts:

1 A board, which allows the connection, by means ofbindings normally used for ski boots, of the wholesystem to the ski. The shape of the board dependson the steepness of the slope .

© 2005 isea Sports Engineering (2005) 8, 13–25 13

Kinematic and dynamic analysis of a sit-ski to improvevibrational comfort

M. Cavacece, F. Smarrini, P.P. Valentini and L. Vita

University of Rome ‘Tor Vergata’, Department of Mechanical Engineering, Italy

Abstract

This paper reports both procedures for the kinematic design and the results of dynamic analyses ofthree models of sit-ski in order to evaluate their vibrational comfort. The model described in theUS Patent US 6,019,380 has been assumed as a reference in the following kinematic and dynamicanalyses of the new models proposed. The two main features to be considered while designing asit-ski are the manoeuvrability and the range of vision of the driver. These two features appear tobe important considering that the sit-ski is generally used by disabled people (e.g. paraplegic). Thusthe kinematic design phase should account for the fulfillment of these requirements. On the basisof these, three new models have been proposed and herein named: Flex, modified Flex and eight-bar linkage (Smarrini 2003). Once the kinematic synthesis and analysis have been completed thedynamic performance of each model is investigated. For this purpose two kinds of slope profiles aresimulated in order to reproduce the stresses which may likely occur during a downhill race. In par-ticular the position and the acceleration of the seat have been monitored during the simulations.This is important in order to test the range of vision and handling requirements. The seat acceler-ation is also important to evaluate the vibrational comfort of the sit-ski according to the Britishstandard BS 6841 (Griffin 1990). The dynamic simulation is first executed by means of themultibody dynamics code NumDyn3D, then the vibrational comfort analysis is performed usingin-house developed software (Vita 2001, Valentini and Vita 2003).

Keywords: sit-ski, kinematic and dynamic analysis, vibrational comfort

Correspondence address:L. VitaUniversity of Rome ‘Tor Vergata’Department of Mechanical EngineeringVia del Politecnico 100133 RomeItalyTel: +390672597136Fax: +39062021351E-mail: [email protected]

2 The mechanism, which regulates the motion ofthe seat, where the board and the shock absorberare fixed on.

3 The shock-absorber, used to minimize the effectsof the slope roughness, as well as to offset the cen-trifugal force during the bend.

4 The coupler of a four-bar linkage, that acts as asupport for the seat and the eventual footrest.Usually, the seat of the sit-ski is made of a singleshell, or more often by two of these linked together.Plastic, carbon fibre or composite materials areoften used. In the agonistic field it is made bymoulds based on the anthropometric measures ofthe driver. The choice of the seat, made of twoshells joined together, influences the movements ofthe upper part of the pilot as required for correcthandling of the curves.

One of the features monitored during the kinematicanalysis is the seat displacement. In fact, for an optimalsight range, the seat should always be kept, as much aspossible, parallel to the ground.

This paper focuses on the kinematic design anddynamic analysis of three new models of sit-ski. Thedynamic performances of these new models have beencompared to the one described by the US Patent US6,019,380. Thus the model described by the USPatent US 6,019,380 is considered as a reference. Thekinematic design criterion of the new models isconcerned with the optimality of the sight range andhandling. During dynamic analysis the position andthe acceleration of the seat are monitored. In particu-lar the Fast Fourier Transform (FFT) of the verticaland horizontal acceleration of the seat are presentedfor each model. Finally the Vibration Dose Value(VDV), according to the British standard BS 6841, hasbeen evaluated for each model of sit-ski.

Optimal features of a sit-ski

The bindings are usually located in the central area of aski. Thus this area, apart from including the centre ofmass of the ski itself, has also to contain the projectionof the centre of mass of the skier. This grants an optimalhandling of the ski. A conventional skier can move thecentre of mass of his/her body by bending their trunk,and by bending their knees, transferring their weight tothe front or the back of the skis as required. This

increases the grip of the cutting edge on the snow, andalso dampens the roughness of the ground and thechanges in slant. It is important that this longitudinalmovement of the centre of mass remains within certainboundaries (i.e. the area between the bindings). As amatter of fact, if the centre of mass of the skier moves,for example, too far backwards, the front of the skiwould decrease the sharing of load with a consequentlack of control of the ski and a possible fall. Thus,another important feature to consider in the sit-skidesign is the avoidance of this situation. Furthermore, itis necessary to account for the performances of theshock-absorber. The purpose of this unit is to smoothenand dampen the seat movement due to the roughness ofthe slope profile. A parameter that needs to be consid-ered is the angle between the seat and the surface of theslope. The closer this angle is to zero, the better thecomfort and the visibility of the slope. For these reasonsfour-bar mechanisms are generally basic elements ofsit-ski structures. By means of an appropriate designconfiguration, four-bar linkage keeps the seat parallel tothe ski and to the ground during movement.

To summarize, the key aspects to take in mindduring the synthesis process are:

1 the position of the centre of mass and of its projec-tion on the ski during motion

2 the handling and the manoeuverbility of the sit-ski(connected with the position of the centre of mass)

3 the angle between the seat and the surface of theslope, in order to grant a wide field of view.

State of the art

This section analyzes the main components of the sit-ski model described in the US Patent US 6,019,380shown in Fig. 1.

These components are:

1 the board (22)1 connected to the monoski (14) bymeans of normal bindings (18)

2 the jointed parallelogram made up of four links (56,58 and the homologues on the opposite plane)

3 the spring-damper system (64)4 the seat (42)5 the foot rest (32).

14 Sports Engineering (2005) 8, 13–25 © 2005 isea

Analysis of a sit-ski to improve vibrational comfort Cavacece et al.

1 The bracketed numbers refer to the numbers reported inFig. 1

The parallelogram permits to absorb the roughness, thechanges in slope and the centrifugal loads during themovement of the ski on the descent and during thebend. The spring force acts in opposition to thedirection of seat rest (44) motion. During all the motion,the seat will always remain parallel to the ground (asshown by the dashed-line (42) and by the path (76)),ensuring a satisfactory sight range. In this model themovement of the connecting rod, and thus of theseat, is controlled only by the movement of the trunk of

the user, leaving the legs and the feet linked to the frame.This choice is claimed by the inventor as an optimiza-tion of the load sharing on the centre of the ski, becauseof a decreased inertial contribution in the movement ofthe ski. On the other hand the angle between the trunkand the thighs of the passenger varies continuouslyduring the movement, having an influence both on thecomfort and on the overall sight range. There is no reg-ulation system for the attachment point of theshock-absorber. It is possible instead to adjust thepositions of the seat and foot rest. A 3D view of thismodel is shown in Fig. 2 where all the components pre-viously described are included.

As shown in Fig. 3 the frame and the connectingrod are parallel to each other in order to grant the par-allelism between the seat and the slope. As aconsequence the range of sight for the user is alwaysnear to the optimal one. However, the centre of massof the system is not bounded inside the area of thebindings. Table 1 reports the main dimensionalfeatures assumed for this mechanism and the verticaland horizontal range of motion of the seat.


Cavacece et al. Analysis of a sit-ski to improve vibrational comfort

Figure 1 Sit-ski described in US Patent US 6,019,380

c) d)

b)a)

Figure 2 Sit-ski proposed models a) US Patent US 6,019,380 b) Flex sit-ski c) modified Flex sit-ski d) eight-bar linkage

Proposed mechanisms

This section describes the main features of innovativesit-ski structures proposed by the authors.

Flex mechanismThis solution is based on a double-rocker four-barlinkage, with the seat attached to the coupler (Fig. 2).

The optimality criterion adopted for the design ofthis model was to maintain the centre of mass of thesystem within the region of the bindings. Thus, thecentre of mass G has been placed on the inflectioncircle of the coupler (Shigley 1980). In order to definethe inflection circle in an analytical way the secondexpression of Euler-Savary has been used

(P0M)2 = ΩM × M′M (1)

where P0 is the instantaneous centre of rotation of thecoupler, M is a generic point belonging to the couplerand Ω is its centre of curvature.

In such a manner the line joining G and inflectionpole I is kept orthogonal to the longitudinal axis of theframe (A0B0), as shown in Fig. 4.

Simultaneously the projection point of G on the framehas been kept symmetrical with respect to the ends ofthe frame link. This model has also been designedconsidering the necessity of adjusting the frame lengthaccording to the features of the track and the personalattitudes of the driver. Thus the attachment point ofthe suspension on the frame could be displaced with aslight variation of the kinematic features previouslymentioned.

As reported in Table 2, the maximum vertical dis-placement of the seat is greater than the one of theprevious model of sit-ski. This leads to a high level ofcomfort and allows wider choice for the dampingcoefficient c and spring stiffness k.



c) d)

b)a)

Figure 3 Trajectories of the moving parts a) US Patent US 6,019,380 b) Flex sit-ski c) modified Flex sit-ski d) eight-bar linkage

Table 1 Dimensional features

Component Value

Bar length 250 mmConnecting rod length 120 mmMaximum rotation of seat 28°Vertical range of seat motion 68 mmHorizontal range of seat motion 104 mm

Eight-bar linkageThis mechanism has eight hinged links, which can besplit into two four-bar linkages. As a consequence, thewhole system should have two degrees-of-freedom.However, a particular element called ‘locker’ (theelement D0A1 in Fig. 6) has been introduced in order todecrease the number of degrees-of-freedom to one.

The second four-bar linkage has all moving linksand shares the connecting rod of the first one.

The advantages of using the eight-bar linkage aresummarized as follows.

1 Due to the kinematic structure and link dimen-sions, the seat is always parallel to the slope.

2 The centre of mass of the skier is always inside thearea between the bindings. This improves thestability of the sit-ski.

3 The linkage ensures an optimal load/spring forceratio.

4 The whole mechanism is very compact.

Table 4 summarizes the dimensional features of themechanism.



Table 2 Dimensional features of the Flex model

Component Value

Frame length 300 mmFirst rocker length 418 mmSecond rocker length 281 mmCrank length 120 mmCrank angle3 14.25°Max vertical range 17 mm

3w.r.t. the initial position of the frame

G P0

B0A0

I

Figure 4 Inflection circle

Figure 5 Comparison of seat motions

Modified Flex mechanismThis model is based on the same performance require-ments adopted for the design of the previous sit-ski.Thus, apart from the main components alreadypresent, a new structure guide-seat has been intro-duced. This new element is essentially aswinging-block mechanism.

The function of this added mechanism is to maintainthe seat parallel to the slope during all the motion of thesit-ski. This is the main difference with respect to theFlex model. A direct comparison of the two seatmotions is shown in Fig. 5 (left-hand side shows theFlex model, and the right the modified Flex model).

The other advantage is to experience a vertical rangeof motion of the seat greater than with the previousmodel. This should increase the comfort of the sit-ski(Table 3).

Figure 6 shows the four-bar linkage made up of thelocker (D0 A1), the frame (1)2 (C0D0), the left rocker (1)(C0 A1) and the crank (1) (A1B1). The function of thismechanism is to govern the motion of the secondfour-bar linkage and, as a consequence, of the seat inorder to minimize the drift motion and to maintainthe centre of mass inside the bindings area. This four-bar linkage has been designed by means of a kinematicinversion (Di Benedetto & Pennestrì 1993). In partic-ular the following design data have been assumed:

1 the length of the frame of the first four-bar linkageC0D0;

2 the coordinates on the xy plane of the points A1B1

of the crank (1) and the frame (2): the values of thex coordinate of point B1 are chosen in order tominimize the drift motion of the sit-ski. The valuesof these coordinates are reported in Table 5.

With reference to Fig. 7 a rigid triangle has beendrawn between points A1, B1 and C0. Then in the same

way a triangle is drawn between points A2, B2 and C0

and between points A3, B3 and C0. By means ofkinematic inversion these two new triangles are rigidlymoved to the initial position (point A1B1) defining theposition of the fixed hinge C′0 and C′′0. The centre ofthe circle containing the three points C0, C′0 and C′′0represents one of the moving hinges of the four-barlinkage. Applying the same procedure to the otherfixed hinge D0, the position of the second movinghinge is also evaluated. This graphical procedureallows the definition of the dimensions of all the linksof the mechanism for the prescribed motion.

In order to better understand the motion of eachmodel, in Fig. 3 the trajectories of the moving partsare depicted.



Table 3 Dimensional features of the modified Flex model

Component Value

Frame length 300 mmFirst rocker length 418 mmSecond rocker length 281 mmCrank length 120 mmCrank angle4 14.25°Maximum vertical angle 182 mm

4w.r.t. the initial position of the frame

Table 4 Dimensional features of eight-bar linkage model

Component Value

Frame (1) length 100 mmFirst rocker (1) length 249 mmSecond rocker (1) length 249 mmCrank (1) – Frame (2) length 100 mmFirst rocker (2) length 81 mmSecond rocker (2) length 81 mmCrank (2) length 100 mmLocker length 302 mm

A1

A2

A3

C′′ C0

C′ C0

C0

B1

B2

B3

Figure 6 Front view of the eight-bar linkage

Figure 7 Kinematic inversion

2 The number in parentheses represents the four-barlinkage to which the link belongs.

Table 5 Coordinates of crank points

Points X (mm) Y (mm)

A1 240 180A2 255 158A3 270 131B1 156 260B2 162 228B3 167 186

Dynamic analysis

In this section the results of the dynamic analyses of theproposed models are presented. These analyses havebeen useful in order to define not only the dynamicbehaviour of the model under investigation, but also thevibrational comfort according to the standard BS 6841(1987) (Griffin 1990). The analyses have been executedsimulating the profile of the track by means of twodifferent analytical functions with the following features:

1 medium slope 45°2 periodic variation of the amplitude of the profile:

400 mm along 20 meter of track3 constant velocity of the sit-ski: 72 km/h.

In particular, the analytical expression of the firstprofile is

h = [ – sin ( )] (2)

where H = 400 mm and t is the time.

In order to simulate the loads due to the presence ofice on the slope and imperfections of the track, theoverall profile is obtained by blending profiles of typeof Eq. (2) with straight-lines.

The characteristics of the cycloidal type profiles aresummarized in Table 6.

The cycloidal type of slope profile is plotted in Fig. 8.

The second profile is of the harmonic type. This,when compared to the previous one, simulates harsherslope. The equation used for this purpose is:

h = H1 sin3( ) + H2 sin3( ) (3)

where H1 = 200 mm is the main amplitude,H2 = –20 mm is the noise amplitude and t is the

time.The characteristics of the harmonic type of slopeprofiles are summarized in Table 7. The overall profileis plotted in Fig. 8.

In both of the proposed slopes a null sollecitation isinterposed between each profile (cycloidal orharmonic) at different frequencies. This is useful inorder to have the system dampen out oscillationsbefore receiving further inputs.

πtTL

πtTL

2πtTL

12

πtTL

Hπ

The result of the dynamic simulation is the accelera-tion time history of the attachment point of the seat tothe sit-ski for each model considered. The accelera-tion of this particular point has been monitored fortwo reasons:

1 in order to define the position of the seat during theuse of the sit-ski on the track

2 in order to evaluate the Vibration Dose Value(Griffin 1990).

Thus the dynamic analyses have been executed foreach model by changing the position of the attach-ment point of the suspension to the frame (where itwas possible). This was in order to investigate theinfluence of the mechanism configuration on theoverall response.

The first mechanism analyzed was the four-barlinkage, as described in the US Patent US 6,019,380.The attachment point of the suspension could not be



Table 6 Cycloidal profile

Sollecitation Time TL [s]

Null from 0 to 2 s -Cycloid from 2 to 6 s 2Null from 6 to 8 s -Cycloid from 8 to 10 s 1Null from 10 to 12 s -Cycloid from 12 to 13 s 0.5Null from 13 to 15 s -Cycloid from 15 to 15.5 s 0.25Null from 15.5 to 17.5 s -Cycloid from 17.5 to 17.75 s 0.125Null from 17.75 to 20 s -

Table 7 Harmonic profile

Sollecitation Time TL [s]

Null from 0 to 2 s -Harmonic from 2 to 6 s 2Null from 6 to 8 s -Harmonic from 8 to 10 s 1Null from 10 to 12 s -Harmonic from 12 to 13 s 0.5Null from 13 to 15 s -Harmonic from 15 to 15.5 s 0.25Null from 15.5 to 17.5 s -Harmonic from 17.5 to 17.75 s 0.125Null from 17.75 to 20 s -

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modified in this mechanism and its configurationparameters and the shock absorber constants are sum-marized in Table 8.

In Fig. 9 are the FFTs of the acceleration timehistories of the attachment point of the seat for bothof the profiles simulated. In both cases there are tworesonant frequencies. The first one, at 1 Hz, corre-sponds to the main frequency of the forcing input.The second one, at 3 ÷ 4 Hz, represents the resonantfrequency of the structure. It is important to notethat the FFT corresponding to the cycloidal slopehas lower values of amplitude than the harmonic one,as expected.

The second model analyzed is the Flex with fourdifferent configurations of the attachment point of thesuspension. Details of these configurations and of theshock absorber parameters are summarized in Table 9.

In Figure 10 are the FFTs of the acceleration timehistories of the attachment point of the seat for bothof the profiles simulated. Even in this case there arethe same differences previously observed between thetwo track profiles. Considering instead the cycloidalprofile only one main peak could be observed insteadof the two peaks observed in the previous model.

The dynamic behaviour is also quite similar foreach configuration of the suspension.

The third model analyzed is the modified Flexwhich has also four different configurations of theattachment point of the suspension. Details of theseconfigurations and the viscoelastic parameters arereported in Table 10.



Time (s)

Hei

ght (

mm

)

Hei

ght (

mm

)

Time (s)

Cycloidal profile Harmonic profile

Figure 8 Cycloidal and harmonic profiles

Table 8 Parameters for the dynamic analysis

Undeformed spring length 296 mmStiffness (k) 78 N/mmDamping coefficient (c) 8 Ns/mmSuspension configuration5 100 mm

5It is the distance of the attachment point from the border of the frame


Stiffness (k) 60 N/mmDamping coefficient (c) 10 Ns/mmFirst configuration6 90 mmUndeformed spring length 357 mmSecond configuration6 60 mmUndeformed spring length 359 mmThird configuration6 140 mmUndeformed spring length 358 mmFourth configuration6 200 mmUndeformed spring length 368 mm



Stiffness (k) 60 N/mmDamping coeff. (c) 10 Ns/mmFirst configuration7 90 mmUndeformed spring length 357 mmSecond configuration7 60 mmUndeformed spring length 359 mmThird configuration7 140 mmUndeformed spring length 358 mmFourth configuration7 200 mmUndeformed spring length 368 mm




Model 1 – FFT of horizontal acceleration

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Am

plitu

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m s

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Harmonic profileCycloidal profile

Hz

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Model 1 – FFT of vertical acceleration

Harmonic profileCycloidal profile

Am

plitu

de (

m s

–2)

Hz

Figure 9 FFT of the accelerations of the first model

Flex – FFT of horizontal acceleration (harmonic profile)

Am

plitu

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m s

–2)

Hz

Conf 1Conf 2Conf 3Conf 4

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Flex – FFT of vertical acceleration (harmonic profile)A

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Flex – FFT of horizontal acceleration (cycloidal profile)

Am

plitu

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Flex – FFT of vertical acceleration (cycloidal profile)

Am

plitu

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m s

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Hz


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Figure 10 FFT of the accelerations of the Flex model

In Fig. 11 are reported the FFTs of the accelerationtime histories of the attachment point of the seat forboth of the track profiles simulated. The dynamicbehaviour of the sit-ski has some differences whencompared with the Flex model. With reference to thecycloidal slope, the FFTs of the horizontal accelera-tions of the two models are similar. The FFTs of thevertical accelerations appear more sensitive to theconfiguration changes of the suspension than theFlex model. Considering the harmonic profile bothof the FFT characteristics (vertical and horizontal)are strongly dependent on the configuration of thesuspension.

The last model analyzed is the eight-bar linkage infive different configurations of the suspension. Theshock absorber parameters and details of theseconfigurations are summarized in Table 11.

In Fig. 12 are reported the FFT of the accelerationsof this last model. The dynamic behaviour is similarfor each configuration except configuration numberfive which is more critical than the others. It should beobserved that this model has the maximum value ofacceleration amplitude (corresponding to the ‘critical’configuration number five) lower than the othermodels. This feature affects also the vibrationalcomfort of the system as reported in the next section.

Vibrational comfort

Generally it is not easy to define the vibrational dis-comfort, because it is in some way a personalperception. What is apparent to anyone is that dis-comfort depends on the vibration frequency. At lowfrequencies the whole body responds as a rigid system,



Modified Flex – FFT of vertical acceleration (harmonic profile)

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Modified Flex – FFT of vertical acceleration (harmonic profile)

Modified Flex – FFT of horizontal acceleration (cycloidal profile)

Am

plitu

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m s

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Modified Flex – FFT of vertical acceleration (cycloidal profile)

Am

plitu

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Figure 11 FFT of the accelerations of the modified Flex model

increasing the occurence of reaching resonance condi-tions for each part of the body (e.g. abdomen, thorax,shoulder and so on) and amplifying the discomfort.The other two main parameters are the magnitude ofthe vibration and the exposure time. The possible con-sequences of exposure to vibrational discomfort forlong and frequent periods are tiredness, disturbed per-ception and several pathologies. For these reasons, it isimportant to define a reliable procedure for evaluatingvibrational comfort. Many international standards tryto give an objective evaluation of the vibrationalcomfort. ISO 2631(1974), slightly amended in 1982(International Organization for Standardization1982), suggested complex and restrictive methods forassessing some effects of vibration. It used anaveraging method to evaluate vibration severity andwas, therefore, unsuitable for assessing shocks, tran-sients or non-stationary random vibration. These




Stiffness (k) 60 N/mmDamping coefficient (c) 10 Ns/mmFirst configuration8 45 mmUndeformed spring length 136 mmSecond configuration8 65 mmUndeformed spring length 133 mmThird configuration8 85 mmUndeformed spring length 132 mmFourth configuration8 105 mmUndeformed spring length 133 mmFifth configuration8 125 mmUndeformed spring length 136 mm


Eight bar – FFT of horizontal acceleration (harmonic profile)

Am

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Conf 1Conf 2Conf 3Conf 4Conf 5

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Eight bar – FFT of vertical acceleration (harmonic profile)


Am

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Eight bar – FFT of horizontal acceleration (cycloidal profile)


Eight bar – FFT of vertical acceleration (cycloidal profile)

Am

plitu

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Figure 12 FFT of the accelerations of the eight-bar model

three last items could be managed by the BritishStandard BS 6841 (1987) which is applicable to theevaluation of all the types of oscillatory motion(British Standards Institution 1987). According to BS

6841, which is then the most advanced in this field, thestandard parameter is the Vibration Dose Value(VDV). The expression for the VDV is

VDV = [ ∫t = T

t = 0a4(t)dt]1/4

(4)

where a(t) is the frequency-weighted acceleration timehistory and T is the period of time over whichvibration may occur. The ‘maximum safe exposure’ isset as a VDV value equal to 15 ms–1.75. Above this limita further exposure to vibration will be accompanied byan increased risk of injury.

In order to evaluate the VDV, the response of avirtual model of a dummy has been monitored. Thedummy is made up of thirteen rigid bodies connectedtogether by means of kinematic pairs. The code,written in Fortran language, was already experimentallyvalidated for the vibrational comfort analysis of caroccupants (Valentini and Vita 2003). The computedVibration Dose Values for each model proposed aresummarized in Table 12. These values refer to theharmonic profile which is the harsher one. Even if thelimit value of VDV is far to be reached for each of themodels of sit-ski analyzed, the last one (eight-barlinkage) is the best in regard to vibrational comfort andis in agreement with the results of the dynamic analyses.

Conclusions

This paper addressed the kinematic design and thedynamic analysis of sit-ski with classic and innovativekinematic structures.

In particular, three new models, called Flex,modified Flex and eight-bar linkage, have been hereinproposed. The performance of the classic sit-ski modelpresented in the US Patent US 6,019,380 has beencompared with the new structures.

Through numerical simulations the dynamic per-formance of different models has been compared by

means of different quality indices. An in-housedeveloped code, named DAViD (DynamicAutomotive Virtual Dummy), has been used for thispurpose (Valentini and Vita 2003). The code is basedon a multibody approach (Haug 1989). Each of the sit-ski models has been implemented together with ahuman body model. The virtual dummy is made up oftwelve rigid bodies linked together by means of elevenkinematic pairs. Moreover three viscoelastic elementshave been modelled to represent the muscular elasticityof elbow and knee articulations and torso. The outputof the code concerns the acceleration time history of theattachment points of the seat to the sit-ski, of each bodysegment and, as stated by the BS 6841, the overall VDV.The input is represented by the track profiles asdescribed in the dynamic analysis section.

The Vibration Dose Value (VDV), evaluatedaccording to BS 6841 standard, is summarized inTable 12 for each model proposed. From thenumerical simulations it appears that the eight-barlinkage model has superior capabilities with respect tothe other structures tested. In particular it has thelowest values of acceleration FFT, for all seatconfigurations and for both of the tracks simulatedand it is also confirmed by the overall VDV(3.35 ms–1.75). This means that the vibrations perceivedby the skier are dampened by the sit-ski structure.Moreover the angle between the seat and the surfaceof the slope is quite near to zero during the simulation.This means that an optimal visibility is ensured evenfor a harsh slope profile such as the harmonic one.These results obtained are in agreement with theintentions pursued during the synthesis phase.

Acknowledgements

The authors wish to acknowledge Professor EttorePennestrì of University of Rome Tor Vergata for hishelpful advice during the development of this work.

ReferencesBritish Standards Institution (1987) Measurement and

evaluation of human exposure to whole–bodymechanical vibration and repeated shock, BS 6841,London.

Di Benedetto, A. and Pennestrì, E. (1993) Introduction to theKinematics of Mechanisms (1st edn) Casa EditriceAmbrosiana, Milano, Italy. (in Italian)



Table 12 VDV of sit-ski models

Sit-ski VDV

US 6,019,380 5.12 ms–1.75

Flex 9.45 ms–1.75

Modified Flex 4.21 ms–1.75

Eight-bar linkage 3.35 ms–1.75

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Griffin, M. (1990) Handbook of Human Vibration, AcademicPress Inc., San Diego CA, USA.

Haug, E.J. (1989) Computer-Aided Kinematics and Dynamicsof Mechanical Systems, Vol. I, Allyn & Bacon, pp. 48–104.

International Organization for Standardization (1982)Guide for the evaluation of human exposure towhole–body vibration, Geneva, Switzerland.

Shigley, J.E. and Uicker, J.J. (1980) Theory of Machines andMechanisms, McGraw-Hill Book Co., New York, USA,pp. 167–230.

Smarrini, F. (2003) Kinematic and dynamic optimization ofmechanisms for sit-ski, Master thesis, University ofRome, Tor Vergata (in Italian)

Valentini, P. and Vita, L. (2003) David – a multibodyvirtual dummy for vibrational comfort analysis of caroccupants, Virtual Nonlinear Multibody Systems W.Schiehlen and M. Valasek (eds) Kluwer AcademicPublisher, Dordrecht, The Netherlands, NATO ScienceSeries II: Mathematics, Physics and Chemistry, Vol.103, pp. 253–262.

Vita, L. (2001) Development and implementation of a 3Dcalculation code for the study of dynamics forapplication to the interface man/vehicle, master thesis,University of Rome Tor Vergata. (in Italian)












Kinematic and dynamic analysis of a sit-ski to improve vibrational comfort

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