The animal "Lynx" in different languages.

*rydjь, so as to distinguish it from the homonymic root *lisъ which already referred to another animal (fox)

Ryś was also called rysiec, so not so similar to lis. Also probably only in Polish we have now ryś/lis pair. In other Slavic languages I see short "ryś" and long "lis" - liška, lisica etc.
Furthermore it's rather a bad idea to make ryś similar to *rydjь to distinguish it from lis, because well… lis is rudy or ryży (about a colour). When I say "I saw ryżego in the forest" everyone will be sure that I saw a fox rather than lynx.

What Brückner writes about ryść:

ryść, wyjątkowo i rycki (por. slertl i sierzchl), stale w szóstym przypadku: ryścią, ryclicią, 'wielkim kłusem'; z niepierwotnem ry-zamiast rzi- (odwrotnie jak w rzygać-, tak samo tryzna i i.); cerk. ristati i riskati, 'cwałować', rus. ristat' i rysim! '; ale rysak pożyczka z rus. rysak, 'kłusak'. Pień rit-; lit. ritu, risti, rileti, 'toczyć wkoło, katulać', railas, 'jeździec' (nie z niem. reiten, Reiter, pożyczone, bo rojtmm-kas, 'obowiązany do służby konnej', zachodzi w aktach białoruskich już z początku 16. wieku, raitiniczia, 'bogini jazdy', u Łasickiego), rai-czio/i; 'katulać'; ale riszczia, o 'cwa-łowuniu', pożyczka, ristas, 'szybki'. Pień rit- urobiony od ri-, p. rój. Czy nie stąd lit. rytas, 'poranek'?; ind. rlti- o 'ruchu, płynięciu', retas-, 'uplaw'. Inni wywodzą od wreit-, anglosaskie wridlian, 'kręcić'.

Polish - ryść - great trot
OCS - ristati, riskati - gallop, career
Russian - ristat', rysim - trotter
? - railas - rider
Belarussian - raitiniczia - godess of raiders
Ind. - rlti- - flow, movement
root rit- - roll, roll the wheel, turn

Now compare this with Polish:
skręt - turn
kręcić - turn, twist, spin
rychły - early, speedy
"ruszyli rysią" - "they moved fast" - from old Polish literature

Aaaand Sanskrit:
cakrikA f. disc
cAkrika adj. circular
cAkrika m. driver
rIti f. diction
rIti f. current
rIti f. line
rIti f. motion

And now the best part

etymonline.com:

Richard
masc. proper name, Middle English Rycharde, from Old French Richard, from Old High German Ricohard "strong in rule," from Proto-Germanic rik- *"ruler" (see rich) + harthu "hard," from *PIE *kar-o- (see hard (adj.)). "One of the most popular names introduced by the Normans. Usually Latinized as Ricardus, the common form was Ricard, whence the pet form Rick, etc." ["Dictionary of English Surnames"]

See rich they say. OK.
etymonline.com:

rich (adj.)
Old English rice "strong, powerful; great, mighty; of high rank," in later Old English "wealthy," from Proto-Germanic rikijaz (cognates: Old Norse rikr, Swedish rik, Danish rig, Old Frisian rike "wealthy, mighty," Dutch rijk, Old High German rihhi "ruler, *powerful, rich," German reich "rich," Gothic reiks "ruler, powerful, rich"), borrowed from a Celtic source akin to Gaulish rix, Old Irish ri (genitive rig) "king," from *PIE root *reg- "move in a straight line," hence, "direct, rule" (see rex).

The form of the word was influenced in Middle English by Old French riche "wealthy, magnificent, sumptuous," which is, with Spanish rico, Italian ricco, from **Frankish *riki "powerful,"** or some other cognate Germanic source.  

Old English also had a noun, rice "rule, reign, power, might; authority; empire." The evolution of the word reflects a connection between wealth and power in the ancient world. Of food and colors, from early 14c.; of sounds, from 1590s. Sense of "entertaining, amusing" is recorded from 1760. The noun meaning "the wealthy" was in Old English.  

"move in a straight line," movement! Signal's clean!

Polinized version of Richard is Ryszard. And this name "feels" very Slavic. Why? Because diminutive form is: Rysiek, Ryś!
Ryś is powerful and moves fast!

And when we speak about power: etymonline.com:

rickshaw (n.)
"small, two-wheeled carriage drawn by a man," 1885, shortened form of jinrikisha (1873), from Japanese jin "a man" + riki "power" + sha "carriage." The elements are said to be ultimately from Chinese. The full word first appears in English publications in Japan and was said to have been a recent innovation there. Kipling, whose ghost story helped popularize it, wrote it 'rickshaw.

rik- is probably Indo-European root which means fast, powerful movement (maybe with sudden turns). As a hunting ryś, as a galloping horse.
Ryś = rex = Rico = Richard = raider

/r/etymologymaps Thread Parent Link - i.imgur.com