Inertial load stabilization in free load exercise machines/Treniruokliu inercines apkrovos stabilizavimas.
Grigas, V. ; Maskvytis, R. ; Tolocka, R.T. 等
1. Introduction
Muscle loading force in exercise machines is created in different
ways, based both on the type of machine and design solutions: weight
stack gravity force, magnetic field resistance [1-6], fluid flow
resistance force, belt friction force, compressed air drag and otherwise
[7].
Besides general purpose, there are also specialized exercise
machines, simulating certain human motions: skiing, rowing and even
swimming [2, 6]. But the most of traditional devices are not enough
accommodated for the improvement or training special or technical skills
of athletes. Such simulators usually train one or more muscle groups,
without giving details of individual muscle activity and avoiding the
excessive load variation during exercise.
Currently simulators with more sophisticated load-generating units
are used more widely, most of them having a feedback between the input
link movement and the generated load [8-9] and the possibility to
control the load. Muscle load can be changed within each exercise step
(cycle) or after performing a certain number of those movements with
regard to functional parameters of the trainee.
There are many companies in the world producing various inertial
force simulation machines: PRECOR [10], BOWFLEX [11], POWER SYSTEMS
[12], KINGS OF CARDIO [13]. The greatest disadvantages of those exercise
machines are uncontrolled muscle load variation due to the action of
inertia forces and the lack of possibility to adopt load to the specific
needs, what undoubtedly may be accessed by using load stabilising and
control devices.
An attempt to improve such exercise machines by introducing
equipment allowing to control or stabilize the load, generated by moving
weight, is described in this paper.
2. Stabilization of inertial load in exercise machines
The most popular scheme of the weight machines is the one where the
athlete lifts weight stack by pushing or pulling the lever, to which the
weight stack is connected by cable guided by pulleys. When moving the
handles of the simulator, the constant mass stack moves with
acceleration, as the result giving a variable load force (Fig.1) [14].
The inertial load can be controlled in simulators in order to make
the exercising process more efficient. It can be stabilized using a
spring-loaded roller, interacting with the flexible coupling of the
simulator (Fig. 2) or controlled by a special actuator that implements
the chosen law of motion (Fig. 3).
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
[FIGURE 3 OMITTED]
Load stabilization possibilities by means of a spring-loaded roller
can be proved by using the model, shown in Fig. 4.
[FIGURE 4 OMITTED]
The spring - loaded roller motion can be described by the following
equation
cy = 2 (G + m[[??].sub.1])cos [[alpha].sub.0] (1)
where c is the spring stiffness; G is load weight; m is load mass;
[[alpha].sub.0] is nominal span angle (assumed that [alpha]
[approximately equal to] [[alpha].sub.0]); y and [y.sub.1] are weight
and roller displacement
[y.sub.1] = y - 2s (2)
where s is the handle displacement.
The solution for harmonic excitation s = [s.sub.0]sin [omega]t is
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
where g is the acceleration of gravity; [[omega].sub.0] = c / 4m is
the natural frequency of the dynamic system.
Solution (3) allows us to define the force acting on the handle
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Finally the condition of stabilizing effect of inertial load may be
defined
c >8m. (5)
3. Experimental test bench and measurement equipment
For the experimental research of weight machine equipped with a
spring - loaded roller stabilizer the test bench was designed by means
of 3D CAD software So lidWorks (Fig. 5).
According to computer model the experimental test bench has been
made meeting the principle of operation of inertia load exercise machine
(Fig. 6). Five steel plates, each weighing 1.3 kg, are used for the
loading. To check mathematical model described in Section 2 the exciter
is designed consisting of electric motor (power of 0.55 kW, rotation
speed 60 [min.sup.-1]) with gearbox and crank mechanism, giving the
harmonically varying kinematic excitation on the input
("handle") of the test bench (the duration of loading cycle
and magnitude of kinematic excitation are set similar to the values
obtained when performing exercises of pulling the handle by hand). The
stack of plates is attached to the exciter via the flexible cable guided
by two pulleys. In the middle of the span between pulleys (1.0 m.) the
cable is deflected in perpendicular direction by the spring - loaded
roller.
[FIGURE 5 OMITTED]
To define the main kinematical and force parameters the measuring
equipment was implemented (Fig. 6.) to the test bench. Thus the input
force ("on handle" or near the force generator) has been
measured by tensometric force gauge, attached to the portable
computerised multichannel measuring chain Spider Mobil (HBM, Germany),
and synchronically - the kinematic parameters of movement of the loading
plates, exciter and the stabilizer roller have been measured by means of
3D motion Capture system (Qualisys, Sweden).
[FIGURE 6 OMITTED]
The force gauge S9 (HBM, Germany) was used for the force
measurements: nominal force [F.sub.nom] - 500 N, accuracy class - 0.05,
sensitivity [C.sub.nom] - 2 mV/V, relative tensile/compression
sensitivity difference dzd < [+ or -] 0.1%, nominal shift [S.sub.nom]
< 0.4 mm.
The 3D video MoCap system Qualisys (6 digital infrared cameras
Pro-Reflex) was used for capturing motion parameters (translations,
velocities and accelerations) of characteristic points of the test bench
where the 15 mm diameter reflective markers were affixed. The maximal
measurement frequency of the system 500 Hz (100 Hz frequency was used),
measurement range: 0.2 - 70 meters, horizontal field-of-view:
10[degrees] to 45[degrees], effective resolution 20000x15000 subpixels,
exposure time -100 - 400 [micro]s.
4. Results of experimental tests
During the preliminary research the "exercising" was
simulated by means of the mentioned exciter, generating 1 Hz frequency
and 100 mm amplitude harmonic kinematic excitation on the handle of
exercise machine.
Such tests were carried out with and without the spring-loaded
roller stabilizer. The maximal force amplitude was obtained when the
"exercising" was performed on weight machine in the
"normal" mode, that is with no stabiliser - 112.4 N, while
implementation of the stabilizer reduced maximum values of the force by
20% to 92.3 N (Fig. 7), thus confirming the effectiveness of the
stabilizer.
[FIGURE 7 OMITTED]
After verifying that the system with the stabilizer is running
efficiently, further tests of the weight machine kinematical and force
parameters were performed.
[FIGURE 8 OMITTED]
Namely, the force on the handle has been measured when pulling it
by hand when bending the arm in elbow (mass of the weight stack - 3,9
kg, an athlete's elbow rests on the table during exercise) (Fig.
8), the law of motion of the roller of the stabiliser (Fig. 9) and the
handle of exerciser have been determined (Fig 10 and 11).
For investigations of the system without stabiliser, the law of
input link motion was determined by using the same video equipment, when
the reflective bead was attached to the handle.
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
[FIGURE 11 OMITTED]
5. Conclusions
1. The test bench of the inertial weight machine exerciser with a
spring loaded roller stabiliser has been developed and experimental
research of the kinematic and force parameters has been carried out.
2. The force developed by the inertial weight machine exerciser may
differ significantly in comparison with the nominal value of the weight
of the plates stack because of inertial loading.
3. The force developed by the inertial weight machine can be
effectively smoothened by means of the stabiliser, and controlled by the
additional actuator equipped with the control system.
4. The hand loading, its motion and stabilising system kinematic
properties were determined experimentally and will be used for the
subsequent research.
References
[1.] Bubulis, A.; Jurenas, V. 2008. Piezomechanics. Vilnius. 120p
(in Lithuanian).
[2.] Boyle, M. 2004. Functional Training for Sports. Human
Kinetics. 195p.
[3.] Bondarchuk, A. 2005. Training Methodology and Concepts.
Available from: http://www.hammerthrow.com/training/Bondarchuk
[4.] Carlson, J.D.; Catanzarite, D.M.; St Clair, K.A. 1995.
Commercial Magnetorheological Fluido Devices. Sheffield. 252p.
[5.] Zhurauski, M.; Dragasius, E.; Korobko, E.; Novikova, Z. 2008.
Mechanical properties of smart fluids under com-bined electrical and
magnetic fields, Mechanika 6(74): 21-24.
[6.] Domeika, A.; Grigas, V.; Ziliukas, P.; Vilkauskas, A. 2009.
Unstable simulator of academic rowing, Mechanika 5(79): 48-51.
[7.] Dal Monte, A.; Faina, M.; Faccini, P. 1990. Manmachine system
optimization and specific ergometry. Biomechnics of human movement,
Applications in Rehabilitation, Sports and Ergonomy (Eds. N. Berme,
A.Cappozzo). Bertec Corporation: 431-443.
[8.] Zatsiorsky, V. M. 1995. Science and Practice of Strength
Training. Human Kinetics. 243p.
[9.] Zatsiorsky, V. M.; Kraemer, W.J. 1995. Science and Practice of
Strength Training. -2nd ed. Human Kinetics. 251p.
[10.] PRECOR training equipment. Available from:
http://eu.precor.com/comm/en/istr
[11.] BOWFLEX training equipment. Available from:
http://www.bowflex.com
[12.] POWE SYSTEMS training equipment. Available from:
http://www.power-systems.com
[13.] KINGS OF CARDIO training equipment. Available from:
http://www.kingsofcardio.com
[14.] Tolocka, R.T.; Grigas, V.; Satkunskiene, D.; Eidukynas, V.;
Domeika, A.; Balcikonis, R. 2007. Investigantion of parameters of the
muscles loading and modeling of their generation by exercise machines.
Report A-070627/1. Kaunas. 73p. (in Lithuanian).
Received January 07, 2011
Accepted June 27, 2011
V. Grigas, Kaunas University of Technology, A. Mickeviciaus str.
37, 44239 Kaunas, Lithuania, E-mail: vytautas.grigas@ktu.lt
R. Maskvytis, Kaunas University of Technology, A. Mickeviciaus str.
37, 44239 Kaunas, Lithuania, E-mail: RobertasMaskvytis@yahoo.com
R.T. Tolocka, Kaunas University of Technology, A. Mickeviciaus str.
37, 44239 Kaunas, Lithuania, E-mail: tadas.tolocka@ktu.lt
