Description
We will focus on the static-geometric properties of ideal flat lever designs. The simplest such designs are flat trusses D2, D3 (Fig. 1), and Assur’s groups M3, M4 [1, 2]. On these schemes the hinges, fixed (pinned) in the plane, are marked by crosses; the free (not fixed) hinges are marked by circles. It is clear how to build inductively trusses Dk and Mk for an arbitrary number k of free joints. The hinges allow all relative rotations in the plane of adjacent levers. There may be combined hinges connecting more than two levers. Considering these designs, we will assume that the positions in the plane of the pinned hinges are not changing. A typical design with the scheme Dk or Mk is a flat truss, that is it does not allow continuous movement of the free joints without changing the lengths of the levers. In addition, it has no internal stresses, i.e. is statically determinate. However, our interest will be focused on special structures allowing internal stresses.