Part 2 - Crux
What does a Roman carriage have anything to do with crucifixion? To tell you the truth, it has something to do with the central point of the matter - and of the structure upon which Romans crucified their worst criminals. And it is the central point of the structure that makes the physics of crucifixion work, and enables the prisoner to suffer for days, maybe a week, instead of just a few hours.
But like I said in Part 1, I think the first thing we should look at is how the lexicons define CRUX, which is the Latin word for CROSS.
And so I present to you the Lewis and Short Lexicon entry for Crux.
crux, ŭcis, f. (m., Enn. ap. Non. p. 195, 13; Gracch. ap.
Fest. s. v. masculino, p. 150, 24, and 151, 12 Müll.) [perh. kindred with circus].
A. In gen., a tree, frame, or other wooden instruments of execution, on which criminals were impaled or hanged, Sen. Prov. 3, 10; Cic. Rab. Perd. 3, 10 sqq.—
B. In partic., a cross, Ter. And. 3, 5, 15; Cic. Verr. 2, 1, 3, § 7; 2, 1, 4, § 9; id. Pis. 18, 42; id. Fin. 5, 30, 92; Quint. 4, 2, 17; Tac. A. 15, 44; Hor. S. 1, 3, 82; 2, 7, 47; id. Ep. 1, 16, 48 et saep.: “dignus fuit qui malo cruce periret, Gracch. ap. Fest. l. l.: pendula,” the pole of a carriage, Stat. S. 4, 3, 28. —
A. As a term of reproach, a gallows bird, a hempen rascal, Plaut. Pers. 5, 2, 17.—
B. Transf., torture, trouble, misery, destruction, etc. (so most freq. in Plaut. and Ter., and in the former esp. freq. in connection with mala): aliqua mala crux, tormentor (of a prostitute), Plaut. Aul. 3, 5, 48; cf.: “illae cruces,” Ter. Eun. 2, 3, 92: “quae te mala crux agitat?” what tormentor troubles you? Plaut. Bacch. 4, 2, 2: “abstraxit hominem in maximam malam crucem,” id. Men. prol. 66: “quaerere in malo crucem,” Ter. Phorm. 3, 3, 11.—Prov.: “summum jus antiqui summam putabant crucem,” Col. 1, 7, 2.—Hence, in colloq. lang.: “I (abi, etc.) in malam crucem!” go to the devil! go and be hanged! Plaut. Cas. 3, 5, 17; id. Ps. 3, 2, 57; 4, 7, 86 al.; Ter. Phorm. 2, 3, 21; cf.: Cy. Num quid vis? Me. Ut eas maximam in malam crucem, Plaut. Men. 2, 2, 53; id. Capt. 3, 1, 9.—Without mala: “I in crucem,” Plaut. As. 5, 2, 91.—And ellipt.: “in malam crucem!” Plaut. Cas. 5, 4, 8; id. Ps. 5, 2, 5. —Hence, Ital. croce; Fr. croix.
Also the Elementary Lewis Lexicon entry for the same word.
crux ucis, f
CVR-, a gallows, frame, tree (on which criminals were impaled or hanged), C.—A cross: (mereri) crucem, T.: cruci suffixi: in crucem acti, S.: Non pasces in cruce corvos, H.: pretium sceleris, Iu.—Torture, trouble, misery, destruction: quaerere in malo crucem, T.—Colloq.: i in malam crucem! go and be hanged, T.
From these two entries we get the following for crux:
1. A tree, frame, or other wooden instruments of execution upon which criminals were hanged or impaled;
2. A cross;
3. The pole of a carriage (or wagon or chariot) - see the photo above - ;
4. A term of reproach, a gallows bird, an 'empen rascal;
5. A torture, trouble, misery, destruction;
6. A tormenter;
7. In the colliquilar, an indirect object or an agent in an obscene curse where the recipient is urged to go to utter perdition.
And where does the word come from? According to Lewis and Short, the word appears to be kindred with the Latin word circus! And where does this word circus come from? According to Lewis and Short, it comes from the Greek word κίρκος [kindred with κρίκος; Dor. κίρκος, and κορώνη.
Here are the definitions of these words according to Liddell, Scott and Jones Greek-English Lexicon:
κίρκος: A hawk or falcon, a kind of wolf, a circle, a ring, later the Lat. circus, an unknown stone, a rower or the stroke of an oar, a budding of a black poplar.
κρίκος: A ring, on a horse's breastband, to fasten it to the peg (ἕστωρ) at the end of the carriage-pole, also an eyelet hole in sails, a curtain-ring, a finger ring, a nose ring, an armlet, a link in a chain, a hoop and a ring of a spanner (wrench).
κορώνη: a sea-bird (possibly), a crow, anything hooked or curved, a door-handle, the tip of a bow, the curved stern of a ship, the top of a bow or in gereral an end or a tip, the curved stern of a ship, a coronoid process of the ulna, the crown of a festival; curved, crooked, of the coronoid process of the jawbone, with crumpled horns.
And where do the above three words come from? They appear to come from the Proto-Indo-European root *sker- that means to turn, bend.
Judging by the above, there appears to be a strong correlation with the word crux and somethnig circular, perhaps cylindrical. Particularly when the instrument of execution that impaled people and the tow-pole of a horse-drawn vehicle are both named by that word. In fact, there is an intimate association with the Latin word crux when used in this second sense and the Greek word κρίκος! How crux got to mean cross is a long story and requires an immense amount of investigation. It will be difficult to do it justice on my humble blog but I will make the case with what I have.
There is another theory about the source of the Latin word crux. It was first proposed by the 19th Century German scholar A. Zestermann who was cited by another German scholar, Hermann Fulda in Das Kreuz und der Kreuzigung (1878 CE). He quotes Zestermann as stating the word crux was derived from a Sanskrit word meaning "torturing cram." Unfortunately, Fulda had found out, that all the people who lived between Rome and India, including the Persians, Babylonians, Syrians, Hebrews and the Phoenicians (from whom the Carthaginians were descended) only knew of the plain word meaning "tree or pole/pale/stake." 
In Part 3 I will talk about the modern English use and the ancient Greco-Roman uses of the word crux that have nothing to do with the actual punishment of crucifixion. Because the Romans NEVER CRUCIFIED the way we think they did!
 Fulda, Hermann. Das Kreuz und der Kreuzigung, Breslau, Verlag von Wilhelm Koebner, 1878, p. 112.
Part 3 - Modern English Use and Ancient Quotidian Meanings.
PREVIOUS CRUCIFIXION ARTICLES:
Crucifixion – The Bodily Support - Part 1.
Crucifixion – The Bodily Support - Part 2 - Archaeological Evidence.
Crucifixion - The Bodily Support - Part 3 - Manuscript Evidence and its Similarities to the Imagery of the Caesar Cult.
Crucifixion – The Bodily Support - Part 4 - Physics of Crucifixion.