Dai in Chinese / Japanese...

大東流合気柔術 is Daitō-Ryū Aiki-jūjutsu, a Japanese martial art established by Takeda Sōkaku.

The most famous student of Daitō-Ryū Aiki-jūjutsu is Morihei Ueshiba who later founded the school or branch of martial arts known as Aikido.

Note: 大東流合気柔術 can also be romanized as Daito-ryu Aiki-Jujutsu, Daitou-Ryuu Aiki-Juujutsu or Daito-Ryu Aiki-Jujitsu.

代 is the word used to designate dynasties in Asia.

代 alone can mean generation; age; period; historical era; eon; world; society; reign; era. 代 comes after the name of the dynasty, for example, the Tang Dynasty is the “Tang Dai” in Chinese.

Some have suggested that the word dynasty comes from the Chinese word “dai” (as “dai” sounds like the first syllable of a dynasty). However, the word dynasty is derived from the Greek word δυναστεία (dunasteia) meaning lordship and/or domination.

Sometimes this word is used in a different context where it can mean to represent or substitute. In this case, it can mean representative of; on behalf of; acting for, e.g. to offer incense in place of another.

In ancient Japan, this could also be a “shiro” (a unit of land area equal to one-fiftieth of a tan or about 20 square miles).

無限大の愛 is a Japanese title meaning infinite great love, unlimited great love, or eternal love.

無 means never, not, or like a prefix “un-.”

限 means limited, restricted, or bound.
大 means great or big.
の is a possessive article.
愛 means love or affection.

大光明 is the master symbol “Daikomyo” or “Dai Ko Myo,” which is usually associated with the healing practice of Reiki.

This title can be translated as “Great Bright Light.” This symbol, as used in Reiki, alludes to “Enlightened Nature” or the radiance of a purified soul or deity.

Pronunciations in Chinese and Korean are included above but this title has no meaning except when used by a Reiki practitioner. In fact, this title is not that well known by those outside the Reiki community in Japan.

In Chinese, this would be interpreted as “Great Bright Future” (the second two characters alone create a word that means “bright future” in Chinese).

In Mahayana Buddhism, 四大 represents mahābhūta, the four elements of which all things are made: earth, water, fire, and wind.

This can also represent the four freedoms: speaking out freely, airing views fully, holding great debates, and writing big-character posters.

In some contexts, this can be a university or college offering four-year programs.

To others, this can represent the Tao, Heaven, Earth, and King.

Going back to the Buddhist context, these four elements “earth, water, fire, and wind,” represent 堅, 濕, 煖, 動, which are: solid, liquid, heat, and motion.

菩提心 means Bodhi-mind or Bodhi-heart.

This title represents the will to realize supreme enlightenment. The awakening of the Bodhi-mind is of utmost importance in Buddhist training.

Other definitions include the mind for or of bodhi, the awakened, enlightened mind, or having Buddha-nature.

大力 can mean immense physical strength or great power.

This can also act as an adjective for expressing how energetically or vigorously something is.

This can also be a given name, Dairiki, in Japanese.

大東流 is Daitō-ryū, a Japanese martial art style - usually associated with Aikido.

南無大菩薩 means to submit to or pay homage to the great Bodhisattva.

The last three characters, 大菩薩, can mean bodhisattva-mahāsattva, refer to one who has reached enlightenment but vows to save all beings before becoming a buddha or a high and noble monk.

大道無門 is a Buddhist proverb that means “The Great Way has no entrance,” “The Great Way is gateless,” or “The Great Path lacks a gate.”

This can be translated in many other ways.

This concept was authored within a long sacred text by 無門慧開 (known as Wúmén Huìkāi in Chinese or Mumon Ekai in Japanese). He was a Chinese Chan Master (in Japanese, a Zen Master) who lived between 1183 and 1260 AD. His most famous work was a 48-koan collection titled “The Gateless Barrier” or “The Gateless Gate” (無門關 Wú Mén Guān in Chinese, or 無門関 Mu Mon Kan in Japanese). This calligraphy title is a notable line from this collection.

I like this reference to the source of this proverb: The Gateless Gate 無門關