Upper Extremity Analysis of the Wrist - Fundamentals and Assessment Tools for Occupational Ergonomics - page 856

where: PR ik is the FDP moment arm for the ith finger and kth joint, SR ik is the FDS moment arm
for the ith finger and kth joint, X 1 ¼ 1 for PIP and 0 for all others, X 2 ¼ 1 for DIP and 0 for all

others, X 3 is the joint thickness (mm) from Table 45.5.
Consequently, the pertinent equations are as follows:

PR DIP ¼ 2 : 16 þ 0 : 225X 3 (45 : 15)

PR PIP ¼ 4 : 53 þ 0 : 225X 3 (45 : 16)

SR PIP ¼ 6 : 52 þ 0 : 225X 3 (45 : 17)

PR MCP ¼ 6 : 19 þ 0 : 225X 3 (45 : 18)

SR MCP ¼ 6 : 42 þ 0 : 225X 3 (45 : 19)

Four Cartesian coordinate systems are established to define the locations and orientations of the
tendons and to describe the joint configuration (Figure 45.11). There are two coordinate systems for
both the middle and proximal phalanges and only one system for the distal and metacarpal phalanges.
The y-axis is defined along the long axis of the each phalanx, from the proximal end to the distal end. The
x-axis is defined as perpendicular to the long axis of each phalanx and in the palmar-dorsal plane, from
the palmar side to the dorsal side of the finger bone. Both x- and y-axes have their origins at the center
of the proximal end of phalanx. Note that these definitions are different from that used by An et al. (1979)
in Figure 45.7, Table 45.7 and Table 45.8.
In terms of notation, subscript i refers to fingers, with 1-4 for the index, middle, ring, and little finger,
respectively, subscript j refers to joints, with 1-4 for the DIP, PIP, MP, and wrist joints, respectively, while
subscript k refers to phalanges, with 1-4 for the distal, middle, proximal phalanges, and the metacarpal
bone, respectively.
In terms of model input values, the external force on each phalange of each finger is indicated by F(i,k).
The finger joint flexion angles, measured with reference to straight fingers as the hand is lying flat, are
indicated by (i,u j ). The length of each phalanx for each finger is indicated by L(i,k).
For output variables, the FDP tendon force for each phalanx of each finger is indicated by TP(i,k). The
FDS tendon force for each phalanx of each finger is indicated by TS(i,k). Finally, joint constraint forces
along the X k - and Y k - axes are indicated by Rx k (i,j), and Ry k (i,j), respectively.
To solve for the aforementioned unknown model output variables, a static equilibrium analyses of each
phalanx must be performed. Specifically, the summation of forces acting on each phalanx in the X- and

Distal Phalanx Middle Phalanx Proximal Phalanx Metacarpal Phalanx

Rx 3 (i,3)

Ry 2 (i,2)

Rx 2 (i,2)

Ry 3 (i,3) Rx 4 (i,4)

(i, 2) θ (i, 3) θ

Ry 3 (i,3)

Ry 1 (i,1)

Rx 2 (i,2) Rx 3 (i,3)

(i, 1) Ry 4 (i,4)

θ Ry 2 (i,2)

Rx 1 (i,1)

TP(i,3)

TP(i,2)
TS(i,2)

F(i,3)

TS(i,3) FDP

TP(i,1) F(i,2)

Rx 1 (i,1)

Ry 1 (i,1)

FDS

F(i,1)

FIGURE 45.11 Simple two-dimensional hand model. For symbols and notation, see text. (Reproduced from
Kong, Y.K. Ph.D. Dissertation, Pennsylvania State University. With permission.)