Nanomechanical computing elements which employ rotational symmetry and
motion are designed and analyzed using a bounded continuum model. Fir
st, the Boolean logic functions of NOT, AND, OR, and XOR are realized
using a helical latch, reset springs, and rod assemblies. Building upo
n these components, designs for shifters and two-level logic devices a
re developed. The helical latching mechanism calculates the Boolean ou
tput function as a positional displacement from a known reset state, w
hich occurs exactly once during each 360-degrees instruction cycle. Op
erations of arbitrary word length can be performed by subdividing the
logic disc into sectors where each sector operates on a single bit. Th
roughput can be increased by pipelining multiple-bit operands to yield
a speedup which approaches a maximum value of (n + 2) as compared to
a single-level of non-pipelined logic with n inputs. Generally, speedu
p is bounded by (n + 2)/p where p denotes the number of cycles between
initiations of the pipe. An analysis of gate kinematics is performed
to determine the device geometries and maximum operating frequencies f
or both non-pipelined and pipelined operation.