Decoupling smoothness, accuracy, and kinematic invariance in biological reach: an ablation study of an equilibrium-point controller in a 34-muscle arm model

Engineering controllers solve musculoskeletal reaching but typically violate the kinematic invariants of human reach: bell-shaped speed profiles, near-straight paths, and a peak-velocity time at 40-50 % of movement duration. For the MyoSuite myoArm (20-DoF, 34 Hill-type muscles) we implement a biologically motivated controller combining (i) Feldmans {lambda}-equilibrium-point hypothesis, (ii) a minimum-jerk virtual trajectory{lambda} (t), (iii) a 200 ms visuomotor correction, and (iv) {gamma}-compatible spinal reflexes (Ia, Ib, reciprocal inhibition). Across n = 50 randomised targets the full controller is practically equivalent to an endpoint-PD + spinal baseline (Cartesian PD descending command paired with the same spinal reflex layer; see [&#167;]2.6) on minimum tip error (Cohens d = +0.03; paired Wilcoxon detects only a +10.6 mm residual against a {approx} 100 mm absolute error, well within a pre-defined {+/-}20 mm equivalence margin) while halving peak speed (1.78 vs 3.90 m s-1, d = -7.39, p < 10-15) and reducing jerk by 40 % (d = -1.74). Only the variant with stretch reflexes brings the velocity-peak ratio into the canonical human range (0.40-0.50). Straightness stays below the human reference, so we frame the result as a partial reproduction of the bell-shape and smoothness invariants, not full human-like reach. A factorial ablation (n = 20) decomposes the contributions: virtual trajectory primarily controls smoothness, visuomotor feedback primarily controls accuracy, and reflexes primarily control velocity-peak timing, with two quantifiable secondary effects reported explicitly. An attempted online cerebellar correction in joint or {lambda} space did not improve performance, consistent with -- but not by itself demonstrating -- the cerebellum as a slow inverse-model learner rather than a within-trial steering controller. We release a deterministic_reset patch for a seeding bug in the MyoSuite reach environments (in the versions tested). The result is mechanistic rather than task-optimal: it attributes separable kinematic axes to distinct biological control layers in a 34-muscle arm.