Haptics combined with functional magnetic resonance imaging (Haptic fMRI) can non-invasively study how the human brain coordinates movement during complex manipulation tasks, yet avoiding associated fMRI artifacts remains a challenge. Here, we demonstrate confound-free neural activation measurements using Haptic fMRI for an unconstrained three degree-of-freedom motor task that involves planning, reaching, and visually guided trajectory tracking. Our haptic interface tracked subjects' hand motions, velocities, and accelerations (sample-rate, 350Hz), and provided continuous realtime visual feedback. During fMRI acquisition, we achieved uniform response latencies (reaching, 0.7-1.1s; tracking, 0.4-0.65s); minimized hand jitter (<8mm); and ensured reliable motion trajectories (tracking, <7mm root-mean-square error). In addition, our protocol decorrelated head motion from both hand speed (r=-0.03) and acceleration (r=-0.025), which reliably produced low head motion levels (<0.4mm/s between scan volumes) and a low fMRI temporal noise-to-signal ratio (<1%) across thirty-five scan runs. Our results address the primary outstanding Haptic fMRI confounds: motion induced low spatial-frequency magnetic field changes, which correlate neural activation across cortex; unreliable motions and response latencies, which reduce statistical power; and task-correlated head motion, which causes spurious fMRI activation. Haptic fMRI can thus reliably elicit and localize heterogeneous neural activation for different tasks in motor (movement), pre-motor (planning), and somatosensory (limb displacement) cortex, demonstrating that it is feasible to use the technique to study how the brain achieves three dimensional motor control.