The Wooden Block Rolling on a Circular Wheel

A profound analogy that reveals different modes of contact and energy transmission (勁路 jìng lù) in Tai Chi push hands (推手 tuī shǒu). Let’s explore these two types of rolling contact from both Tai Chi theory and mechanical principles, highlighting the meanings of 沾 (zhān), 粘 (nián), and how contact is maintained or lost.

---

🌀 1. The Wooden Block Rolling on a Circular Wheel — Dynamic, Momentary Contact

(如矩形木頭滾在圓輪上)

This example illustrates a form of 沾 (zhān)—which in Tai Chi means to make initial light contact and follow.

Imagine a rectangular block (矩形木頭) rolling forward over a round wooden wheel (圓輪) beneath it. As the block rolls forward, the wheel also turns and moves. However, due to gravity and inertia, the contact point shifts and is not always fully attached:

• At times, there's full rolling contact—this is similar to when your forearm connects lightly to your partner’s, and the motion of one guides the motion of the other.

• At other times, the block may briefly lift or shift away from the wheel due to acceleration or uneven pressure, resembling a momentary loss of sticking (失粘 shī nián).

From mechanical theory, this relates to rolling friction and variable normal force—the contact force depends on acceleration and distribution of mass. The block and wheel respond to each other indirectly, not from one fixed contact point.

In Tai Chi, this dynamic can reflect intermittent energy linkage, often found in beginners’ push hands—where the partner’s movement is followed but not fully integrated. The energy is not sunk and continuous (氣不貫通).

Classical reference:

「沾者，如影隨形，若即若離。」
"To zhān is to follow like a shadow—seemingly joined, yet occasionally separate."

---

🚆 2. The Train Car and Wheel — Constant Integrated Contact

The second example, where the train car and its wheels move together, reflects a deeper level of Tai Chi connection, aligned with 粘 (nián)—meaning to adhere and synchronize through energy.

• In this case, the train body and wheels are fixed—they share the same axis of motion and acceleration.

• As the wheel rotates, the carriage naturally moves with it, maintaining constant orientation and integrity of connection.

• There is no separation, no slippage, and movement is smooth and unified.

This reflects the Tai Chi ideal of "連綿不斷 (lián mián bú duàn)" — continuity without breakage, and "以心行氣，以氣運身" — using intention to lead qi, and qi to move the body.

Mechanically, this resembles pure rolling motion with axial fixation, where torque and angular velocity are transmitted from the center to the periphery, with the body moving as one integrated system (整體 zhěng tǐ).

In push hands, this is the ideal expression of energy connection (勁連 jìng lián)—the hands, elbows, shoulders, waist, and legs move as a coordinated spiral, rooted in the feet and led by intent (意 yì).

Classical reference:

「粘者，緊而不脫，如膠似漆。」
"To nián is to adhere tightly without detaching, like glue or lacquer."

---

🔁 Comparison & Application

Analogy	Tai Chi Term	Contact Quality	Mechanical Principle	Application in Push Hands
Rectangular block on rolling wheel	沾 (zhān)	Light, variable, shifting	Rolling contact, intermittent normal force	Initial following, partial energy reception
Train carriage and wheel	粘 (nián)	Stable, unified, continuous	Fixed axial rotation, continuous rolling	Advanced sticking, whole-body energy link

---

✅ Summary

• 沾 (zhān) is like rolling contact—initiating connection but not always maintaining it.

• 粘 (nián) is like a fixed axis—deeply joining and sharing the same motion.

• The goal in Tai Chi push hands is to evolve from zhān to nián, from light touch to full-body integration.

• Mechanically, this reflects a shift from variable contact force to stable torque transfer.