Friction-loaded cycle ergometers: Past, present and future

Figures & data

Figure 1. Force acting on the tight (F_T) and slack (F_S) ends of a rope winding around a rotating cylinder.

Figure 2. Braking mechanism of the first friction-loaded ergometers; braking force acting on the flywheel (F_FW) is equal to the difference between tight (F_T) and slack (F_S) forces which were displayed by means of scale.

Note: Pedal rate, F_T, and F_S had to be continuously recorded or adjusted to know the actual work.

Figure 3. Amar’s cycle ergometer; D, P, and R correspond to the dynamometer, platform for weight, and steel ribbon, respectively.

Note: Red and blue arrows correspond to F_T and F_S, respectively.

Figure 4. Thomson brake (drawing adapted from Beaumont, 1889, p. 33; Jervis-Smith, 1915, p. 82).

Notes: L corresponds to the loose pulley and F to the fast pulley, rigidly fixed to shaft S; P: fixation of the tight rope (in red). C: connection between the loose pulley and the rope (in blue) rubbing on the fast pulley.

Figure 5. Fleisch ergometer; F et L fast et loose wheels, C connection between pulley L and belt B that is attached to weight W₂ at the other end.

Notes: F_T and F_S are equal to W₁ and W₂, respectively. For clarity, the distance between L and F has been increased.

Figure 6. A, L_B et L_P arms of forces F_B and P; F_T and F_S, tensions of the tight and slack ends of the belt; O₁, O₂, and O₃, axles of the flywheel, cam, and pulley, respectively; O₄ pivot of the roman steelyard; B, h₁, and h₂ lever-arms of F_S1 and F_S2, respectively; W_c and h_c weight of the cam and its lever arm.

Figure 7. Von Döbeln ergometer.

Note: P center of mass of the pendulum, S force scale, O axle of the pulley.

Figure 8. Monark sinus-balance cycle ergometer.

Notes: O₁, axle of the sinus-balance pulley, O₂, axle of the pulley pressing on the slack belt; W, P, and r_W, weight, center of gravity, and arm lever of the pendulum; F_T and F_S tension of the tight and slack ends; F_SC, tension of the slack belt corrected by the force F_E exerted by the pulley; H, handle for manual adjustment of braking torque. The force scale is not presented; S2 secondary force scale readable by the subject who pedals.

Figure 9. Weight-basket loaded cycle ergometer.

Notes: Radius r_S is smaller than radius r_T. R₁ and R₂, ribbons limiting the vertical displacements of the basket. F_B, F_T, and F_S, forces exerted on the pulley by the basket load, the tight, and slight extremities of the belt-rope, respectively; T turnbuckle.

Figure 10. A, belt in the sinus-balance model; B, belt and rope in the basket-loaded ergometers; C, digging of small grooves in the circumference of aluminum flywheel; D, 3-turn rope.

Note: In red and blue, tight and slack extremities, respectively.

Figure 11. Relationships between μ, F_T, F_S, and error in F_FW expressed as fractions of F_B.

Notes: Data computed for θ = 10.4 rad and r_S/r_T = 0.45. The data corresponding to the studies by Gordon et al. (2004) and Franklin et al. (2007) have been added with the values of k corresponding to ratio F_T/F_S.

Figure 12. In A, time–frequency curves during all-out sprints against different loads on a Monark 864 cycle ergometer; in B, relationship between load and peak frequency (V_peak).

Note: The parabola in B corresponds to the load–power output relationship computed from the linear load–V_peak relationship (P_max = 0.25 V₀F₀). Adapted from Driss & Vandewalle (2013).

Figure 13. Time–power output curves computed during all-out sprints on basket-loaded cycle ergometer against loads equal to 19 N (red curve) and 76 N (blue curve).

Note: Adapted from Driss & Vandewalle (2013).

Figure 14. Relationship between the computed torque exerted on the crankwheel and crank angular speed (or pedal rate) during all-out sprints against two loads (19 N red points and 76 N blue points) in the same subject.

Note: Data adapted from Seck et al. (1995), with permission.

Figure 15. In A, adjustment of the zero; in B, force calibration with a calibrated weight.

Note: The position of the pendulum can be adjusted by deplacing the adjustement weight.

Figure 16. Contact of the frame (F) with the slack extremity of the belt-rope.

Figure 17. In A decomposition of the force F₁ exerted on the pedal into a force F₂ exerted on the crank shaft and a couple C; in B comparison of the mean torque (red line) and the torques exerted on the left (blue dashed line, L) and right crank (blue continuous line, R) during a pedal revolution.

Figure 18. Schematic diagram of the method used in the study by Jones & Passfield (1998) for the comparison of a basket-loaded Monark^TM ergometer (in blue), model 814 (ME) and data of different SRM^TM transducers.

Notes: The SRM^TM transducer crank wheel (S) was driven by a chain from a bicycle wheel driven by a treadmill (T, in red) belt. The SRM^TM crank wheel, in turn, drove the flywheel of the Monark^TM ergometer.

Figure 19. Results of dynamic calibrations of friction-loaded ergometers.

Notes: (A) Comparison of the power output according to the manufacturer (power at flywheel) and power output measured by dynamic calibration; continuous line corresponds to identity line, dotted, and dashed lines error levels equal to 5 and 20%, respectively. (B) Differences between power output a flywheel and calibrated power at crank axle, gray lines correspond to different levels of underestimation (% of power output at flywheel). In red, Cumming & Alexander (1968), mean of 4 Monark ergometers; in blue, Wilmore et al. (1982), 1 ergometer; black points, Maxwell et al. (1998), mean of 35 Monark ergometers, protocol with increasing power output; empty circles, Maxwell et al. (1998), mean of 35 Monark ergometers, protocol with decreasing power output.

Figure 20. Parts of a cycle ergometer that must be maintained (explanations in text); 7, chain adjuster bolt, lateral view.

Figure 21. Example of a mechanism enabling the adjustment of the belt tension by a change in distance between the axes of the pulley (O₁) and the flywheel; O₂, axle of the mechanism; H, handle; N, locking nut.

Figure 22. Braking mechanism consisting of a friction belt made of two belts in series; in red, belt with low friction coefficient (μ₁); in blue, belt with high friction-coefficient (μ₂).

Note: C, connection between the belts.

Figure 23. Variation of the location of the center of mass during half a revolution of the flywheel.

Figure 24. Relationship between ratio μ₁/μ₂ and descent (D) of the basket from a basket weight equal to 2 kg to a weight equal to 8 kg.

Notes: These curves have been computed for a decrease in k from 25 (F_B = 19.6) to 4.28 (F_B = 78.5 N). Ratio μ₁/μ₂ was computed for values of θ₁ (winding of the belt around the flywheel) ranging between 3.14 and 5.7 rad (0.5 ≤ h₂ ≤ 0.9) with a basket weight equal to 2 kg. In red, negative values.

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