Encoder-Resolution Misattribution in Student-Built Engineering Education Robotic Arms: A Laser-Tracker Evaluation Linking Joint Backlash to Path-Accuracy Reliability Bounds

Student-built robotic arms in engineering education are routinely specified by encoder resolution, yet the path accuracy that students actually observe is frequently governed by joint backlash rather than by encoder quantisation. The framework is operationalised through a before-after-control-impact design with an intraclass correlation of 0.64, between-cluster SD of 6.0, and residual SD of 4.5; power was estimated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis indicates that 54 clusters are required to detect a 5-percentage-point effect at 80% power. The contribution is a mechanism-level account of why encoder-resolution claims misattribute the dominant error source in educational robotic arms, together with a reliability-bound formulation that instructors and student designers can apply before hardware is commissioned.