Fig. 8. A dynamic template for climbing. The two degrees of freedom model that
generates the template climbing dynamics shown in
Fig. 7C. (A) Schematic of the
model. (B) Schematic of the motion of the model during two steps (one stride
of period T). In the first step with the right leg, at touchdown
(t=0) the right actuator is maximally extended, and the spring is
un-extended with zero rest length. Touchdown is created by establishment of a
rotationally free pin-joint with the wall. As the actuator length
L(t) decreases, the spring in the leg extends, the foot
freely pivots about the point of contact and the center of mass (COM) is
translated vertically and laterally. The cycle repeats for the left leg. The
actuator changes length sinusoidally such that
L(t)=L0[1+zsin(2
ft)],
where z is the fractional length change and f=1/T
is the stride frequency. The solid vertical line in each panel indicates the
fixed lateral position about which the COM laterally oscillates. The angular
excursion of the body is exaggerated for clarity. Actual angular excursion of
the body relative to vertical is approximately ±3°. The model was
coded and integrated in the Working Model 2D (Design Simulation Technologies,
Inc) simulation environment. The parameters used to generate
Fig. 7C were body mass=2 g,
body dimensions=4 cmx0.95 cm, l1=0.71 cm,
l2=0.84 cm, ß=10°, L0= 1.54
cm, z=0.6, k=6 N m-1,
=0.09 Ns
m-1, f=9 Hz. The attachment duty factor in the model is
0.46.