Rotary-Encoder Quadrature Error in Student-Built CNC Milling Rigs for Engineering Education: A Laser-Interferometer Benchmark Linking Index-Pulse Jitter to Tool-Path Dimensional-Conformance Bounds

Student-built CNC milling rigs used in engineering education typically rely on low-cost incremental rotary encoders whose quadrature signals carry phase, duty-cycle and index-pulse timing errors that are rarely characterised before the machine is released to students. The treatment is methodological and analytical rather than empirical: no student rig was instrumented and no measurement campaign was executed. A formal error model is derived in which quadrature phase error, edge jitter and index-pulse timing variance combine into a per-revolution position uncertainty, and a conformance bound is stated as a function of encoder resolution, jitter variance and commanded feed. The propagation analysis yields closed-form bounds that a laboratory instructor or technician can evaluate from an encoder datasheet and a single index-pulse timing measurement, and it identifies the feed-rate and resolution regimes in which index-pulse jitter, rather than quantisation, dominates the conformance bound. The contribution is a transferable benchmark protocol and a set of derived bounds that make encoder quality an explicit, auditable design parameter in the student CNC rig, rather than an unexamined assumption.