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Networks of Torque Propagation
Figure 2.4:3D Lego structure
generated by our evolutionary process. The underlying physical model is shown.

Our model for a 2D structure of bricks generates a network, called a Network
of Torque Propagation (NTP) consisting of nodes, joints and loads.
 Each node represents a brick and its located at the brick's center of
mass (circles in our figures).
 An additional node represents the ground.
 Each pair of locked bricks gives raise to a joint. The joint has an origin
node, a destination node, an axis of rotation (located at the center of the
area of contact between the bricks) and a maximum torque capacity (depending
on the number of knobs involved). Joints are represented by lines in our figures,
their axis of rotation by stars.
 Loads represent the forces acting on the network. Each has magnitude,
direction, point of application, and entry node. For each brick, a force corresponding
to its weight originates at the center of mass, is applied at the corresponding
node, and points downwards. External forces may have any direction and their
point of application is not necessarily the center of the brick.
Each force, either the weight of one of the bricks or an external load, has
to be absorbed by the joints in the structure and transmitted to the ground.
The magnitude of the torque exerted by each joint j must lie in the interval
[K_{j}, K_{j}], where K_{j} represents
its maximum capacity as deduced from table 2.1.
By separating each 3D joint into two orthogonal and independent 2D joints, which
receive the x and y components of each force, we can project an
entire 3D network model of a brick structure into two orthogonal planes, xz
and yz, generating two 2D NTP's that can be solved separately (figs.
2.4 and 2.5). Thus the problem
of solving a 3D network is reduced to that of solving 2D networks.
Figure 2.5:
Projecting
the 3D structure of fig. 2.4 to the xz and yz
planes, two 2D networks are obtained that can be solved independently.

Next: NTP Equations
Up: Simulating Bricks Structures
Previous: From 2 to 3dimensional
Pablo Funes
20010508