Case 3: Balancing the Load on your Fingertips

In this case the hand is holding a tray with an outstretched forearm (Fig 1a). A free body diagram shows the forces acting on the tray (Fig 1b). The tray exerts a force downward under the influence of gravity. The fingers support a force upward to support the tray while the thumb exerts a force downward to prevent the tray from rotating out of the hand. As a result the fingers have to support the weight of the tray and the force of the thumb. The wrist must exert a torque or moment to support both the weight of the tray and the weight of the hand (Fig 1c)

holding a tray between the fingers and thumb with an outstretched forearm holding a tray between the fingers and thumb with an outstretched forearm holding a tray between the fingers and thumb with an outstretched forearm
(a)(b)(c)
Fig 1: The tray is balanced on the fingertips with the thumb pressing down on the inside of the fingers to counteract the weight of the tray acting outside of the fingers (a). A freebody diagram shows the resultant forces and moments acting on the tray (b), where:
Ffingers = force exerted by the fingers
W = weight of the tray (and its contents)
X1 = distance between the center of gravity, c/g, of the tray and the finter tips
MW = moment produced about the fingertips by the tray
Fthumb = force exerted by the thumb
X2 = distance between the force exerted by the thumb and the fingertips
Mthumb = moment produced about the fingertips by the thumb
The free-body diagram shows the the moments produced about the wrist by the weight of the tray and the weight of the hand, (c), where:
Whand = weight of the hand
X4 = distance between the center of gravity, c/g, of the hand and the wrist
Mwrist = Moment produced about the wrist by the hand
X3 = distance between the center of gravity, c/g, of the tray and the wrist
Mtray = Moment produced about the wrist by the hand
Mwrist = Moment produced about the wrist by the muscles

Estimate the forces acting on the thumb

Fthumb = W×X2 / x1

This relationship is based on the basic law of physics that all forces acting in any given direction must all add to zero and all moments acting about any given point must add to zero. It will be assumed that the weight of the tray and the forces exerted by the fingers and thumb are acting in a vertical direction.

Ffingers = W + Fthumb
Fthumb × X2 = W×X1
Fthumb= W× X 1 / X2

Estimate the forces acting on the fingers

Ffingers - W - Fthumb=0
Ffingers = W + Fthumb=0

Estimate the Moment acting about the wrist

W×X3 + Whand×X4 - MLoad = 0
MLoad = W×X3 + Whand×X4

The center of gravity of the hand is approximately 50% of the hand length and the mass of the hand is approximately 0.5% of body weight (various sources summarized by LeVeau 1992).

Similarly, the moment can be computed for the elbow and shoulder, but it will be necessary to adjust for the angles of the forearm and arm.

Thumb force and finger force calculator

Pinch force calculator:

Fthumb = × ) /   Required thumb force

Finger force: = Tray weight + FThumb force

Wrist moment: Mwrist=W×X3 + Whand×X4

Determining force locations

  1. The weight of the tray and its' contents, W, can be determined by weighing them.
  2. The distance, x1 can be estimated from a photograph or direct measurement (see Fig 2).
  3. The distances x2, can be estimated by measuring the distance between the tray center of gravity, c/g, and the fingertips.
  4. Estimates of the center of pressure measurements should consider the relative strengths of the fingers. See work by: Barter et al, (1956); Hazelton, et al. (1985) Figueroa-Jacinto, et al. (2018). It can be seen in Fig 2 that the force produces contact with the pulp of the fingers and the thumb is aligned closer to the 2nd finger than the 3rd due to the greater strength of the 1st and 2nd fingers than the 3rd and 4th.
  5. If the tray contents are uniformly distributed, the c/g will be at the geometric center of the tray and x1 can be measured the same way as x1.
  6. If the load is not uniformly distributed, it will be necessary to find the center of gravity, c/g. This can be done mathematically based on the weight of the tray and the objects on the tray and their location with respect to the edge where the tray is to be held.
    1. Calculate the sum of the weights of the tray and objects on the tray: Wtotal = ∑mi.
    2. Calculate the sum of the moments produced by each object about the edge where tray is grasped: Mtotal = ∑xi×wi.
    3. Calculate the distance between the edge of the tray and the over c/g as: Mtotal/Wtotal.
  7. The c/g also can be determined by:
    1. Measuring the total weight of the tray, Wtotal
    2. Measuring the weight at opposite edges of the tray, w1 and w2
    3. and the distance between w1 and w2.
    4. Measuring the distance between w1 and Wtotal
    5. Computing: x2 = (w2 × x1) / Wtotal
Finger locations for tray holding horizontal tray
Fig 2: The center of finger pressure, center of thumb pressure, and center of gravity of the tray and its contents are estimated and measured with a ruler.

Relative load -- %MVC

Relative load or percent maximum voluntary contraction:
%MVC = strength demand (force or moment) / strength capacity × 100%

Thumb strength will generally be the most limiting factor for holding the tray. Thumb strength data published by Kroemer and Gienapp (1970) correspond most closely to the action of the thumb for holding the tray. Their data are based on USAF pilots, though, and may not be representative to a broad work population. These data can be scaled based on corresponding AF pilot grip strengths and that of other populations.

The thumb action to hold the tray also corresponds to that in lateral pinch. There are a number of strength studies of lateral pinch, and i should be possible to find something relevant to most problems, e.g., Mathiowetz et al. (1985). See: Task Hand Strength Demands and Capacities, Section 4.3

Example Problem:

Use the following data to estimate the forces on the thumb and fingers:

References:

  1. Barter JT, Frey EI, Truett B (1956). Anthropometry and Biomechanics of the Hand. unpub. ms., Wright-Patterson Air Force Development Center Aero. Med. Lab., Ohio. (Cited in: Damon, A., H. w. Stoudt and R. A. McFarland (1966). The Human Body in Equipment Design. Cambridge, MA, Harvard University Press, p. 221.
  2. Figueroa-Jacinto R, Armstrong T, Zhou W (2018): Normal force distribution and posture of a hand pressing on a flat surface. J Biomech. 79:164-72.
  3. Hazelton F, Smidt G, Flatt A, Stephens R (1975): The influence of wrist position on the force produced by the finger flexors. Journal of Biomechanics. 8(5):301-6.
  4. Kroemer K, Gienapp E (1970): Hand-held device to measure finger (thumb) strenght. J Appl Phys. 29(4):526-7.
  5. LeVeau B (1992) William's and Lissner's biomechanics of human motion. Pennsylvania: Saunders" pp:206-213.
  6. Mathiowetz V, Kashman N, Volland G, Weber K, Dowe M, Roger S (1985): Grip and pinch strength: Normative data for adults. Arch Phys Med Rehab, 66:69 – 76. link