Nanomechanical computing elements which employ rotational symmetry and motion are designed and analyzed using a bounded continuum model. First, the Boolean logic functions of NOT, AND, OR, and XOR are realized using a helical latch, reset springs, and rod assemblies. Building upon these components, designs for shifters and two-level logic devices are developed. The helical latching mechanism calculates the Boolean output function as a positional displacement from a known reset state, which occurs exactly once during each 360 degrees instruction cycle. Operations of arbitrary word length can be performed by subdividing the logic disc into sectors where each sector operates on a single bit. Throughput 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, speedup 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 for both non-pipelined and pipelined operation.