Tipless Mechanism: Distributed Force Innovation

• Tipless mechanisms are defined by the absence of localized tips, using distributed force and torque control in mechanical, robotic, and economic systems.
• In robotics, they employ innovations such as differential gears, radial-layer jamming, and parallelogram linkages to achieve robust grasping and adaptive stiffness.
• In blockchain protocols, tipless mechanisms streamline transaction fees by replacing user-selected tips with fixed, protocol-determined incentives for better predictability.

A tipless mechanism is a technical construct or protocol wherein the concept of a "tip" is omitted and replaced by alternative means of imparting or controlling force, torque, or incentive in mechanical, robotic, or economic systems. This term appears in diverse contexts, including atomic force microscopy (AFM), robotic grasping and manipulation, variable-stiffness actuators, and blockchain mechanism design. The defining attribute is the absence of localized "tips"—whether physical (tool/finger) or algorithmic (user-selected tip payment)—in favor of distributed force application, protocol-set constants, or broader contact surfaces.

1. Mechanical and Robotic Tipless Mechanisms

Tipless mechanisms in robotics are exemplified by designs where grasping, manipulation, or actuation is achieved without reliance on dedicated fingertip geometry. Mechanical solutions employ extended or distributed contact regions and may combine kinematic linkages, gear-driven transitions, or frictional enhancements to compensate for the lack of tips.

For instance, the 1-DOF robotic gripper with infinite self-twist capability (Nishimura et al., 2022) achieves grasping and twisting via a differential gear mechanism, passively switching between modes based on the measured fingertip force. When the tip force is low, the gripper grasps; above a threshold (set by preloader friction), the entire gripper rotates, performing "twist grasping." This twist mode enables exponentially increased payload via multiple wraps, as described by:

$$f_{obj} = B_1 B_2 f_g, \quad B_1 = e^{2\pi\mu(n-1)}, \quad B_2 = e^{2\pi\mu}$$

where $n$ is the number of wraps and $\mu$ the friction coefficient. The mechanism does not depend on finger tips alone, but on extended contact, making it particularly suitable for grasping flexible thin objects where traditional antipodal grasping fails.

Similarly, the design of mechanical tools for 2-finger parallel grippers (Hu et al., 2019) utilizes dual symmetric parallelograms with torsion springs at internal joints. The absence of a dedicated tip is compensated by the parallelogram's capacity for stable, parallel motion transmission, and interchangeable tooltips offer adaptability for a wide variety of manipulation tasks. The tipless or "skillful" function is realized at the tool level rather than at the finger/actuator, facilitating versatile, actuator-independent manipulation.

2. Variable-Stiffness Tipless Mechanisms: Radial-Layer Jamming

The radial-layer jamming mechanism for string configuration (Mukaide et al., 2019) is a paradigm for tipless stiffness modulation in soft robotics. The mechanism employs concentric cylindrical walls actuated via central wire tension. Friction generated at cylindrical interfaces yields tunable stiffness and holding torque:

$T_{\text{radial}} = \sum_i \mu R_i T$

Unlike comb jamming, the holding torque does not decrease at distal joints, supporting long, slender, or tipless structures. Experimental results demonstrate persistent holding torque along the structure (e.g., $\sim 0.39~\text{Nm}$ at the fourth joint), confirming suitability for multi-DOF manipulation without the necessity of specialized tip components.

3. Tipless Mechanism in Blockchain Transaction Fee Protocols

In economic or algorithmic settings, the tipless mechanism refers to a transaction fee system where the notion of a user-specified tip is replaced by a protocol-determined, hard-coded tip (Roughgarden, 2021). Users specify only their fee cap, and the protocol uniformly applies a base fee ($r$) plus a tip ($\delta$) to all included transactions:

$\text{User payment per unit} = r + \delta$

This mechanism is analytically described as "tipless" in that it excludes variable, user-selected tip bidding, shifting the selection criterion to the posted-price protocol. Incentive compatibility properties are rigorously analyzed:

• DSIC (Dominant-Strategy Incentive Compatibility): Truthful bidding reduces to setting the fee cap equal to user value; strategic manipulation offers no utility improvement.
• MMIC (Myopic Miner Incentive Compatibility): Miners maximize income by block-filling, as receipts per transaction are invariant.
• OCA-proofness (Off-Chain Agreement Proofness): Collusion resistance is achieved except during demand spikes or periods where the base fee is insufficiently recalibrated.

Comparison with EIP-1559 and classical auction schemes demonstrates that tipless protocol design achieves highest simplicity for users and predictable allocation for miners under normal demand. However, resilience to off-chain collusion may be compromised under excess demand unless base fees dynamically track equilibrium levels.

Mechanism	MMIC	DSIC	OCA-proof
Tipless	Yes	Yes	Yes (usual)
EIP-1559	Yes	Yes*	Yes
FPA	Yes	No	Yes
SPA	No	Yes	No

(* "Yes (usual)" indicates exceptions during demand spikes.)

4. Calibration and Measurement in Tipless AFM Cantilevers

In AFM instrumentation, tipless cantilevers—i.e., beams with no or extremely short probe tips—can have their torsional eigenmode calibrated accurately via non-invasive thermal noise methods (Thorén et al., 2018). The absence of a pronounced tip simplifies the analytical relation between flexural and torsional stiffness:

$$\kappa_\mathrm{t} = 0.15 \, k_\mathrm{f} b^2 \left(\frac{\omega_{0t}}{\omega_{0f}}\right)^2$$

where $k_\mathrm{f}$ is flexural stiffness, $b$ the beam width, and $\omega_{0t}, \omega_{0f}$ the torsional and flexural resonance frequencies, respectively. This empirical ratio is constant for tipless or short-tipped beams, eliminating the need for direct torsional noise measurement and supporting robust calibration for dynamic nanoscale friction imaging.

5. Implications, Applications, and Design Trade-offs

Tipless mechanisms are advantageous where distributed contact or actuation is required, or where complexity, fragility, or variable demand calls for protocol-level simplicity and robustness. In robotics, they enable manipulation of objects that evade traditional point-contact designs. In fee mechanisms, tipless protocols reduce user strategic complexity and facilitate incentive alignment, although dynamic demand may challenge collusion resistance.

A plausible implication is that tipless concepts enable generalization of gripper and transaction protocol design by reducing reliance on localized actuation or variable user input, focusing instead on distributed control, fixed parameters, and modular adaptability. Mechanical implementations (e.g., parallelogram linkages, radial jamming, infinite twist graspers) and algorithmic protocols (e.g., tipless auction rules) share the attribute of homogenizing the force or incentive distribution, subject to context-dependent trade-offs in flexibility, collusion resistance, and peak performance.

6. Summary of Key Formulas and Mechanisms

Context	Tipless Mechanism Formula	Mechanism Attribute
Robotic Twist Grasp	$f_{obj} = e^{2\pi\mu(n-1)} e^{2\pi\mu} f_g$	Payload amplification via wraps
Transaction Protocol	User pays $r + \delta$, tip is protocol-set	Bidding simplicity, DSIC/MMIC/OCA
AFM Cantilever	$$\kappa_\mathrm{t} = 0.15 k_\mathrm{f} b^2 \left( \frac{\omega_{0t}}{\omega_{0f}} \right)^2$$	Stiffness calibration for tipless beams
Radial-Layer Gripper	$T_{\text{radial}} = \sum_i \mu R_i T$	Constant torque across joints

These mechanisms collectively demonstrate the structural and algorithmic basis for tipless designs, applicable in both physical manipulation and market protocol engineering.