Trajectory of the body centre of pressure and centre of mass during initiation and termination of gait

This chapter discusses strategies that older and younger people employ to negotiate stairs based on experiments performed on an instrumented staircase in lab environment aiming at identifying ways to reduce stair fall risk for the elderly. Stair negotiation was found to be more demanding for the knee and ankle joint muscles in older than younger adults, with the demand increasing further when the step-rise was higher. During descent of stairs with higher step-rises, older adults shifted the centre of mass (COM) posteriorly, behind the centre of pressure (COP) to prevent forward falling. A decreased step-going resulted in a slower descent of the centre of mass in the older adults and standing on a single leg for longer than younger adults. A greater reliance on the handrails and rotation of the body in the direction of the handrail was also observed when the step-going was decreased during descent, which allowed this task to be performed with better dynamic stability, by maintaining the COM closer to the COP. These findings have important implications for stair design and exercise programs aiming at improving safety on stairs for the elderly.

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Optimal wing hinge position for fast ascent in a model fly

Journal of Fluid Mechanics ◽

10.1017/jfm.2018.337 ◽

2018 ◽

Vol 849 ◽

pp. 498-509

Author(s):

R. M. Noest ◽

Z. Jane Wang

Keyword(s):

Stability Analysis ◽

Body Length ◽

Weak Dependence ◽

The Body ◽

Simplified Model ◽

Centre Of Mass ◽

Flight Stability ◽

Hinge Position ◽

Stroke Amplitude ◽

Aerodynamic Lift

It was thought that the wing hinge position can be tuned to stabilize an uncontrolled fly. However here, our Floquet stability analysis shows that the hinge position has a weak dependence on the flight stability. As long as the hinge position is within the fly’s body length, both hovering and ascending flight are unstable. Instead, there is an optimal hinge position, $h^{\ast }$, at which the ascending speed is maximized. $h^{\ast }$ is approximately half way between the centre of mass and the top of the body. We show that the optimal $h^{\ast }$ is associated with the anti-resonance of the body–wing coupling, and is independent of the stroke amplitude. At $h^{\ast }$, the torque due to wing inertia nearly cancels the torque due to aerodynamic lift, minimizing the body oscillation thus maximizing the upward force. Our analysis using a simplified model of two coupled masses further predicts, $h^{\ast }=(m_{t}/2m_{w})(g/\unicode[STIX]{x1D714}^{2})$. These results suggest that the ascending speed, in addition to energetics and stability, is a trait that insects are likely to optimize.

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Centre of pressure versus centre of mass stabilization strategies: the tightrope balancing case

Royal Society Open Science ◽

10.1098/rsos.200111 ◽

2020 ◽

Vol 7 (9) ◽

pp. 200111

Author(s):

Pietro Morasso

Keyword(s):

Degrees Of Freedom ◽

Sensory Feedback ◽

Sagittal Plane ◽

Control Variable ◽

Variable Number ◽

Body Parts ◽

Centre Of Mass ◽

Centre Of Pressure ◽

Feedback Controllers ◽

Neuromotor Control

This study proposes a generalization of the ankle and hip postural strategies to be applied to the large class of skills that share the same basic challenge of defeating the destabilizing effect of gravity on the basis of the same neuromotor control organization, adapted and specialized to a variable number of degrees of freedom, different body parts, different muscles and different sensory feedback channels. In all the cases, we can identify two crucial elements (the CoP, centre of pressure and the CoM, centre of mass) and the central point of the paper is that most balancing skills can be framed in the CoP–CoM interplay and can be modelled as a combination/alternation of two basic stabilization strategies: the standard well-investigated COPS (or CoP stabilization strategy, the default option), where the CoM is the controlled variable and the CoP is the control variable, and the less investigated COMS (or CoM stabilization strategy), where CoP and CoM must exchange their role because the range of motion of the CoP is strongly constrained by environmental conditions. The paper focuses on the tightrope balancing skill where sway control in the sagittal plane is modelled in terms of the COPS while the more challenging sway in the coronal plane is modelled in terms of the COMS, with the support of a suitable balance pole. Both stabilization strategies are implemented as state-space intermittent, delayed feedback controllers, independent of each other. Extensive simulations support the degree of plausibility, generality and robustness of the proposed approach.

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The dispersion of contaminant released from instantaneous sources in laminar flow near stagnation points

Journal of Fluid Mechanics ◽

10.1017/s0022112074000498 ◽

1974 ◽

Vol 66 (4) ◽

pp. 753-766 ◽

Cited By ~ 3

Author(s):

P. C. Chatwin

Keyword(s):

Boundary Layer ◽

Laminar Flow ◽

Bluff Body ◽

Velocity Potential ◽

Tangent Plane ◽

The Body ◽

Centre Of Mass ◽

Stagnation Points ◽

Molecular Diffusivity ◽

Instantaneous Source

This paper considers the dispersion of a cloud of passive contaminant released from an instantaneous source in the steady two-dimensional laminar flow near the forward stagnation point on a bluff body. The body is replaced by its tangent plane y = 0 with x measuring distance along the plane. Far away from y = 0 the flow is irrotational with velocity potential ½l(x2 – y2), where l is a positive constant. When the boundary layer is ignored the equation governing the distribution of concentration can be solved exactly. Consequences of this solution are that for large times the centre of mass moves parallel to the body at a speed proportional to exp (lt) while the cloud spreads out along the body symmetrically about the centre of mass with the magnitude of the spread also proportional to exp (lt). However, this solution is unrealistic because most of the contaminant is confined to a layer adjoining the body of thickness of order (k/l)½, where k is the molecular diffusivity, and this layer normally lies within the boundary layer, which is of thickness of order (v/l)½, where v is the kinematic viscosity. An approximate analysis, based on ideas similar to those supporting the Pohlhausen method in boundary-layer theory, suggests that when the boundary layer is taken into account the conclusions above remain true provided that exp (lt) is replaced by exp (βlt), where β is a constant depending on v/k. Calculations give values of β ranging from 0·73 when v/k = 0·5 to 0·10 when v/k = 103.

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Stable hovering of a jellyfish-like flying machine

Journal of The Royal Society Interface ◽

10.1098/rsif.2013.0992 ◽

2014 ◽

Vol 11 (92) ◽

pp. 20130992 ◽

Cited By ~ 37

Author(s):

Leif Ristroph ◽

Stephen Childress

Keyword(s):

High Speed ◽

Motion Tracking ◽

The Body ◽

Flapping Wings ◽

Wing Size ◽

Centre Of Mass ◽

Hovering Flight ◽

High Speed Video ◽

Aerodynamic Model ◽

Aerodynamic Surfaces

Ornithopters, or flapping-wing aircraft, offer an alternative to helicopters in achieving manoeuvrability at small scales, although stabilizing such aerial vehicles remains a key challenge. Here, we present a hovering machine that achieves self-righting flight using flapping wings alone, without relying on additional aerodynamic surfaces and without feedback control. We design, construct and test-fly a prototype that opens and closes four wings, resembling the motions of swimming jellyfish more so than any insect or bird. Measurements of lift show the benefits of wing flexing and the importance of selecting a wing size appropriate to the motor. Furthermore, we use high-speed video and motion tracking to show that the body orientation is stable during ascending, forward and hovering flight modes. Our experimental measurements are used to inform an aerodynamic model of stability that reveals the importance of centre-of-mass location and the coupling of body translation and rotation. These results show the promise of flapping-flight strategies beyond those that directly mimic the wing motions of flying animals.

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Energetically optimal running requires torques about the centre of mass

Journal of The Royal Society Interface ◽

10.1098/rsif.2012.0145 ◽

2012 ◽

Vol 9 (73) ◽

pp. 2011-2015 ◽

Cited By ~ 7

Author(s):

James R. Usherwood ◽

Tatjana Y. Hubel

Keyword(s):

Large Body ◽

The Body ◽

Moment Of Inertia ◽

Mechanical Work ◽

Vertical Force ◽

Centre Of Mass ◽

Pitch Moment ◽

Tail Structure ◽

Reaction Forces ◽

Long Head

Bipedal animals experience ground reaction forces (GRFs) that pass close to the centre of mass (CoM) throughout stance, first decelerating the body, then re-accelerating it during the second half of stance. This results in fluctuations in kinetic energy, requiring mechanical work from the muscles. However, here we show analytically that, in extreme cases (with a very large body pitch moment of inertia), continuous alignment of the GRF through the CoM requires greater mechanical work than a maintained vertical force; we show numerically that GRFs passing between CoM and vertical throughout stance are energetically favourable under realistic conditions; and demonstrate that the magnitude, if not the precise form, of actual CoM-torque profiles in running is broadly consistent with simple mechanical work minimization for humans with appropriate pitch moment of inertia. While the potential energetic savings of CoM-torque support strategies are small (a few per cent) over the range of human running, their importance increases dramatically at high speeds and stance angles. Fast, compliant runners or hoppers would benefit considerably from GRFs more vertical than the zero-CoM-torque strategy, especially with bodies of high pitch moment of inertia—suggesting a novel advantage to kangaroos of their peculiar long-head/long-tail structure.

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