KENDAMA — an independent reimplementation ========================================= This is an independent reimplementation of a traditional Japanese toy and of the competition rules published for it. It is NOT endorsed by, affiliated with, or connected to the Japan Kendama Association, GLOKEN, or Yamagata Koubou. No code, art or text was taken from any of them; the rules are quoted, in short, with attribution to the documents they come from. THE ORIGINAL ------------ Kendama in its modern form descends from the 日月ボール ("sun and moon ball"), devised in 1918 by 江草濱次 (Hamaji Ekusa) of Kure, Hiroshima. It was filed on 1918-10-01 and registered as a utility model on 1919-05-14 — the date Japan now marks as Kendama Day. It was the first to combine the two previously exclusive kinds of play, spearing the ball and catching it in a cup, in one tool with three cups and a spike. The Japan Kendama Association (公益社団法人日本けん玉協会) was founded in 1975 by the children's author 藤原一生 (Issei Fujiwara) in Tanashi, Tokyo, and held the first All-Japan Kendama-dō Championship in 1979. The competition kendama descends from the S-type designed in 1975 by 新間英雄 (Hideo Shinma) of the Tokyo Kendama Club; the F-type of 1978 added the twin string holes in the cup body, and the F16-2 of 2001 moved that hole off the ken's central axis. The Association's certified manufacturer is 山形工房 (Yamagata Koubou), Nagai City, Yamagata. WHAT THIS IS, AND WHAT DIFFERS FROM THE REAL THING -------------------------------------------------- Faithful, because it is documented and quoted: - the eleven kyu events and their order, and the number of successes each grade needs - the maximum of ten attempts per event, and stopping once the count is reached - the 準初段 (jun-shodan) rank between 1-kyu and 1-dan, and its nine events - the twenty dan events and the full success matrix for 1-dan to 6-dan - what counts as a catch: the whole outer circumference of the cup face in contact with the ball, and the spike entering the hole completely - the three-second balance hold, the 15 s to start and 40 s to finish - moshikame at 135 repetitions a minute, one repetition per cup-to-cup move, and two landings in a row on the same cup ending the attempt - the permitted alternative orders for 日本一周 and 世界一周 - ふりけん's one full ball turn toward the performer, and the prohibition on horizontal rotation in とめけん - the cup diameters, the ken's height, the cup body's span, the woods, and the string length guidance Reconstructed, because no source that could be opened states it: - the ball's diameter (60 mm is on a reference site, not on the Association's or the maker's pages) - the hole's diameter and depth, the spike's length and base diameter, the cup body's profile, the handle's diameter, the slip-stop's position, the cup depth for the certified model - where the string leaves the ball relative to the hole — DERIVED here from two Association documents rather than guessed - the size of the cup body's off-axis string hole offset (its existence and direction are documented; its magnitude is not) - every mass, because no kendama mass is published anywhere - the restitution and friction of ball against ken - the hand: stiffness, damping, force and torque limits, and reach Differs by design: - a side view in a single plane of hand control, played with a mouse - the ken is a bounded 6-DOF servo, not a person's grip, knees and body - the string is inextensible with zero restitution - eleven kyu events are played; the dan syllabus is shipped as data and displayed only - 灯台 is playable but the engine's own solver could not find a plan for it SOURCES, WITH THE REVISION READ ------------------------------- Japan Kendama Association (kendama.or.jp), all read 2026-09-12: - けん玉道級・段位審査規程, rev. 2018-03-18 (first enacted 1978-05-05, 11 amendments) - 級・段位審査規程 別紙類 (別表第1/2/3), tables rev. 2017-03-12 - 級・段位認定試験細部実施要領, rev. 2024-06-06 (enacted 2000-10-29) - 級・段位認定試験及び公式戦におけるルールの原則, rev. 2019-05-10 (enacted 2012-05-05) - 級・段位認定試験種目における技の解説と注意事項, rev. 2019-05-10 (enacted 2000-10-29) - 公式戦使用けん玉規程, rev. 2019-05-10 (enacted 1978-05-05) - 全日本けん玉道選手権大会 競技規則 and 選技規則, both enacted 2024-04-09 - 全日本けん玉道もしかめ選手権大会 競技規則, enacted 2024-10-03 - 競技審判関係 質問と回答, updated 2025-06-30 - /tricks/123-2/ (the 123-trick list), /tricks/nyumonkyu/, /tricks/for_beginners/, /archives/ninteikendama/ NOTE: the syllabus is VERSIONED and has changed repeatedly. The examination regulation carries eleven amendment dates, the kyu table five, the dan table eight. A trick list found elsewhere is very likely a different revision. The Association also publishes at least three different "official" trick lists (the 2000 book of 100, the current list of 123, and the syllabus events), which do not agree in scope. Equipment figures: - 山形工房 / Yamagata Koubou, kendama.co.jp — overall length, woods, comparison models - GLOKEN shop listing for the certified 大空, gloken-shop.net — ken height 160 mm, cup body span 70 mm, 大皿 42 mm, 小皿 38 mm, 中皿 35 mm, ken beech, ball cherry - Japanese Wikipedia, 日本けん玉協会 — the 60 mm ball diameter, and nothing else Mechanics: - D. Baraff, Physically Based Modeling: Rigid Body Simulation, SIGGRAPH '97 course notes — the impulse law, eq. 8-6 to 8-18 - C. Hecker, Game Developer, March 1997 — the two-dimensional effective-mass form, eq. 9 - A. Ruina & R. Pratap, Introduction to Statics and Dynamics — boxes 13.1 and 13.2, the reduced mass and the energy lost in a restitution impulse, and the warning that restitution is not a material constant - S. L. Loney, Dynamics of a Particle and of Rigid Bodies, Ch. XV Ex. 2, and E. J. Routh, Art. 170 Ex. 1 — the string-snatch on a rigid body, worked in closed form. The physics oracle is validated against both before it is trusted. Robotics (both read in full, both openly readable): - Shidi Li, Robot Playing Kendama with Model-Based and Model-Free Reinforcement Learning, arXiv:2003.06751 - M. Bujarbaruah, Z. Zheng, A. Shetty, M. Sehr, F. Borrelli, Learning to Play Cup-and-Ball with Noisy Camera Observations, arXiv:2007.09562 NEITHER models the re-tautening of the string. That gap is why this build exists. Materials: - H. Sugihara, M. Noguchi, S. Okushima, K. Nomura, Wood Research No. 39 (1966), Kyoto University, Table 1 — specific gravity 0.65 for Fagus crenata, oven-dry - E. Gallego, Á. Ruiz, P. J. Aguado et al., International Agrophysics 34 (2020) 485-494, Tables 7 and 8 — wood-on-wood restitution 0.62 ± 0.058 and friction 0.49 ± 0.07, measured on pressed wood pellets, NOT on a kendama COULD NOT BE OPENED, AND SO IS NOT CITED ----------------------------------------- - Miyamoto/Kawato et al., Neural Networks 9(8) 1996 — paywalled - Nakano/Wada/Kawato, JSME Trans. C 59(558) 1993 — image scan, no text layer - Kober & Peters, Machine Learning 84 (2010) — publisher interstitial - kendamaworldcup.com — a JavaScript-only application serving no rule text - every British and European kendama association domain tried — DNS-dead - both stores.jp shops — HTTP 403 - Japanese cherry's density — not found in any openable source CORRECTIONS MADE BY THIS BUILD ------------------------------ 1. To a common statement: "the taut-string impulse annihilates only the velocity component along the string" is the point-mass statement. What it annihilates is the relative radial velocity of the two ANCHOR points; the ball's anchor is on its surface, so the same impulse spins the ball. 2. To a common assumption: "Kendama dimensions are standardised by the JKA and should be documented." They are not. The only numeric dimensional requirement in any JKA regulation is that the ken be at least 15 cm long. There is no specification document. 3. To a hypothesis this build itself wrote down: the release-speed window's edges are NOT given by a reachability bound on the ball's apex. The model's own successes violate it. 4. To common description: the JKA's ban on rotating the ball in とめけん is, per its own 2025 judging Q&A, a ban on HORIZONTAL rotation — a まわしとめけん — not on all rotation. 5. To common description: plain 灯台 is a straight vertical lift of the ken without rotating it, not a throw. The throwing versions are 一回転灯台 and 二回転灯台. ART, CODE AND FONTS ------------------- All artwork is drawn from the engine's own dimensions by tools-images.py (PIL) and by a hand-written WebGL renderer; no third-party library is vendored and no external font, script, stylesheet or image is loaded. Code is MIT-licensed; see LICENSE.txt.