"Max's Cone — A Hypothetical New-Type Wrench for Piano Tuning"

[themaximillyan]

Introduction
At first glance, the weight of 3.3 kg seems excessive for a tuning wrench. Readers might wonder, "Why so heavy?" or "How could this possibly be useful?" However, this weight is intentionally chosen to demonstrate the practical manufacturability of the device on a lathe.
This article explores the hypothetical tool called "Max's Cone," a novel concept in the evolution of tuning wrenches. It is designed as an experimental approach, introducing a new way of interacting with tuning mechanics.
Max's Wheel: Max's Wheel is a mechanism that combines a first-class lever, a rotating element, and a wedge-shaped component. Its unique feature is the positioning of the support point (the axis of rotation) above the force application point (the hand), creating a distinctive kinematic scheme. The applied force transforms into rotational motion (torque) transmitted to the socket in a series of fast, sequential impulses. This action mimics the effect of impact tools without abrupt energy accumulation and release. Such a construction allows for force amplification.
Historical Context: The tuning of musical instruments has evolved significantly over time. From the hammer—a simple tool for the additional "tapping" to the T-shaped and today L-shaped wrench, which has been the standard for over a century. This article highlights a hypothetical alternative to these traditional tools: a design that offers greater rationality under specific conditions.
Design Philosophy: The shape of "Max's Cone" reflects engineering thought and invites philosophical analysis. It redistributes force efficiently through its "integrated structure," where the post and rim function as a unified system. This solution harnesses friction forces to benefit the system, establishing a new level of convenience and functionality.
Future Perspective: While the weight of the wrench can be reduced by using composite materials (halving or even reducing it to one-third), this article opts for oak—a classic material that emphasizes durability, reliability, and the realistic possibility of lathe production. This choice underlines not just how the tool could function but how it could be crafted.
The "Max's Cone" article invites readers not only to see the hypothetical tool but to reflect on its physical, philosophical, and engineering aspects. Although it may never become a practical solution, its purpose is to inspire and broaden the horizons of thinking, uncovering new possibilities in traditional tuning practices.
Part 1: Geometry of the Design
Key Parameters:
CONE:
•   Upper Radius: 25 cm
•   Lower Radius: 6 cm
•   Height: 5.5 cm
•   Material: Solid oak, density 700 kg/m³
•   Weight: ~3.3 kg
•   Structural Feature: "Integrated post," merging the base and rim into a cohesive system
AND
SOCKET:
The socket is a standard head for tuning pins.
Type: standard octagonal socket. (SEIKO)
Length: 57 mm (including threaded part).
Diameter of the octagonal part: suitable for pin with a diameter of 6.9–7.1 mm.
Height above pins: 4.5 cm.
The socket freely "passes" between the pins, without creating interference. Strong threads provide stability under maximum loads.
Operational Description: The "wheel" serves as the central element, allowing even force distribution on the tuning pin through three application methods:
1.   Rotation with both hands moving clockwise.
2.   Parallel rotation along the strings.
3.   Alternating rotation using either hand.
Physical Design:
•   The conical structure minimizes angular wobble typical of conventional T-shaped and G-shaped wrenches.
•   The "integrated post" creates system density, stabilizing force application under maximum loads.
Part 2: Force Calculations

Friction Force:
The friction force ( Ft ) is calculated using the following formula:
Ft = ΅ Χ N

Where:
•   ΅ = 0.3 – Coefficient of friction (metal-wood)
•   N = 50 N – Normal force
Result:
Ft = 0.3 Χ 50 = 15 N

Torque:
The torque (M) is calculated as:
M = F Χ r

Where:
•   F = 100 N – Applied force
•   r = 0.25 m – Radius of the rim
Result:
M = 100 Χ 0.25 = 25 N⋅m

Gravitational Force:
The gravitational force (Fg) acting on the wrench is given by:
Fg = m Χ g

Where:
•   m = 3.3 kg – Mass of the wrench
•   g = 9.81 m/s² – Gravitational acceleration
Result:
Fg = 3.3 Χ 9.81 ≈ 32.37 N

Tension Force of the String:
The tension force (T) in the string is calculated using:
T = (F Χ L) / A

Where:
•   F = 200 N – Applied force
•   L = 1.5 m – Length of the string
•   A = 0.0001 m² – Cross-sectional area of the string
Result:
T = (200 Χ 1.5) / 0.0001 = 3,000,000 N
Thread Pressure:
The thread pressure ( σ ) is calculated with:
σ = F / A

Where:
•   F = 1666.67 N – Applied force
•   A = π Χ D Χ h ≈ 785.4 mm² – Area of the thread cross-section
Result:
σ = 1666.67 / 785.4 ≈ 2.12 MPa
Part 3: Conclusion
Applying force to the pin use "Max Cone" with two hands
Real-world resistance: On most grand pianos, the friction force to hold the pin is up to 15 N m, which is significantly lower than the maximum resistance of 25 N m for which the "Max Cone" is designed.

Required tuning force: To "budge" the pin from its place with a resistance of 15 N m, the force applied with two hands can be reduced:
Explanation: With a resistance of 15 N m, the tuner can rotate the tuning pin by applying a force of 60 N with both hands, which is 1.5 times lower than the maximum value of 100 N, which is calculated for a maximum load of 25 N m.

Conclusion: "Max Cone" copes with tuning the tuning pins with a reserve at a resistance below 15 N m, providing the tuner with the convenience of applying force from two hands, one hand or palms. This makes the tool not only hypothetically functional, but also convenient for everyday work.
"Max's Cone" not only demonstrates engineering innovation but also showcases the potential for reimagining traditional tools. The inclusion of an "integrated post" and a conical geometry provides a fresh perspective on how force is distributed during tuning tasks. Technical calculations confirm its ability to handle resistance up to 25 N·m, making it capable of tackling even challenging settings.
Philosophical Aspect: This project illustrates the remarkable synergy between human creativity and AI-driven innovation. "Max's Cone" is not merely a hypothetical tool but an instrument to inspire further exploration of mechanical and engineering possibilities.
https://www.academia.edu/128649561/Scientific_Article_Maxs_Cone_A_Hypothetical_New_Type_Wrench_for_Piano_Tuning_