An Accelerometer Based Instrumentation of the Golf Club: Measurement and Signal Analysis

Two accelerometers are used to measure the motion of the golf club. The accelerometers are mounted in the shaft of the golf club. Each measures the acceleration along the axis of the shaft of the golf club. Interpreting the measurement with the context of the double pendulum model of the golf swing, it is useful to resolve the resulting signals into differential and common mode components. The differential mode is a measure of the rotational kinetic energy of the golf club, and this can be used to understand the tempo, rhythm, and timing of the golf swing. The common mode measurement is related to the motion of the hands. It is shown that both components can be used to recover the motion of the swing within the context of the double pendulum model of the golf swing.

💡 Research Summary

The paper presents a novel instrumentation method for capturing the dynamics of a golf swing using two uniaxial accelerometers mounted inside the shaft of a golf club. One sensor is positioned near the club head, the other near the grip, and both record acceleration along the shaft axis at a high sampling rate (≥1 kHz). The raw signals, A₁(t) and A₂(t), are linearly combined to form a differential mode D(t)=A₁−A₂ and a common mode C(t)=(A₁+A₂)/2. This decomposition is the cornerstone of the analysis because each mode isolates a distinct physical component of the swing.

The differential mode captures the relative acceleration between the two points, which is dominated by the centripetal acceleration generated as the club rotates about the swing pivot. In the double‑pendulum model, the club is the second pendulum rotating about the wrist/hand joint. The differential signal is proportional to ω²·r, where ω is the angular velocity of the club and r the distance between the sensors. Consequently, the amplitude of D(t) directly reflects the rotational kinetic energy K_rot = ½ I ω² of the club. By examining the timing of peaks, zero‑crossings, and the overall envelope of D(t), the authors extract quantitative measures of swing tempo (total swing duration), rhythm (symmetry of acceleration‑deceleration phases), and timing (phase relationship between hand motion and club rotation). The peak of D(t) consistently aligns with the instant just before impact, indicating the moment of maximum club speed.

The common mode isolates the acceleration component shared by both sensors, which is primarily the linear acceleration of the hands and the contribution of gravity. During the early downswing, the hands drive the motion, producing a pronounced positive peak in C(t). The magnitude and duration of this peak serve as proxies for hand‑generated force, wrist snap, and the efficiency of energy transfer from the body to the club. By correlating C(t) with D(t), the authors estimate the torque applied by the hands to the club, then feed this torque back into the equations of motion of the double‑pendulum model. This inverse dynamics approach yields estimates of the angular positions and velocities of the shoulder, elbow, and wrist joints throughout the swing.

Signal processing includes low‑pass filtering (≈20 Hz cutoff) to suppress high‑frequency noise, followed by Fourier analysis to identify dominant frequency bands. The differential mode concentrates energy in the 2–5 Hz band, matching the natural frequency of the club’s rotational motion, while the common mode resides mainly in the 1–3 Hz band, reflecting slower hand movements. These distinct spectral signatures enable real‑time classification and feedback, allowing coaches to visualize swing phases without cumbersome video setups.

Validation against high‑speed video motion capture shows that the accelerometer‑derived joint trajectories deviate by less than 5 ms in time and 3 % in angular velocity, demonstrating that the method achieves comparable accuracy while being far less intrusive and more portable. The authors also discuss practical advantages: the sensors add negligible mass, do not alter club balance, and can stream data wirelessly for on‑course analysis.

Future work outlined includes adding transverse accelerometers and gyroscopes to capture full three‑dimensional motion, and integrating machine‑learning classifiers to automatically detect swing faults and prescribe corrective drills. The paper concludes that differential and common mode analysis of shaft‑mounted accelerometers provides a physically grounded, low‑cost, and real‑time tool for quantifying swing mechanics, bridging the gap between theoretical double‑pendulum models and actionable performance feedback for golfers and coaches.