Etymology
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promenade (n.)

1560s, "a leisurely walk, a walk for pleasure or display," from French promenade "a walking, a public walk" (16c.), from se promener "go for a walk," from Late Latin prominare "to drive (animals) onward," from pro "forth" (see pro-) + minare "to drive (animals) with shouts," from minari "to threaten" (see menace (n.)).

Meaning "place for walking" is from 1640s; specifically "walkway by the sea" (from late 18c.); British sense of "music hall favored by 'loose women and the simpletons who run after them' " [The Observer, Jan. 18, 1863, in reference to the Alhambra in Leicester Square] is attested from 1863. Sense of "a dance given by or at a school" is from 1887.

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amble (n.)
"an easy walking gait (of a horse), the gait of a horse when both legs on one side are in motion at the same time," from Old French, from ambler (see amble (v.)). Of persons from c. 1600.
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peripatetic (n.)

mid-15c., Peripatetik, "a disciple of Aristotle, one of the set of philosophers who followed the teachings of Aristotle," from Old French perypatetique (14c.) and directly from Medieval Latin peripateticus "pertaining to the disciples or philosophy of Aristotle," from Greek peripatētikos "given to walking about" (especially while teaching), from peripatein "walk up and down, walk about," from peri "around, about" (see peri-) + patein "to walk, tread" (see find (v.)). Aristotle's custom was to teach while strolling through the Lyceum in Athens.

In English, the philosophical meaning is older than that of "person who wanders about" (1610s). As an adjective, "walking about from place to place, itinerant," from 1640s, often with a tinge of humor. Related: Peripatetical.

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rattan 

also ratan, type of climbing palm with tough, flexible stems that are economically valuable for making chair-bottoms, walking sticks, baskets, etc., 1650s, from Malay (Austronesian) rotan, rautan, according to OED from raut "to trim, strip, peel, pare."

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allure (v.)
"tempt by the offering of something desired," c. 1400, from Anglo-French alurer, Old French aleurer "to attract, captivate; train (a falcon to hunt)," from à "to" (see ad-) + loirre "falconer's lure," from a Frankish word (see lure), perhaps influenced by French allure "gait, way of walking." Related: Allured; alluring.
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gradient (n.)
"steep slope of a road or railroad," 1835, principally in American English, probably from grade (n.) by analogy of quotient, etc. [OED]. It was used 17c. as an adjective, of animals, "characterized by walking;" in that case it is probably from Latin gradientem, present participle of gradi "to walk."
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walk (n.)

c. 1200, "a tossing, rolling;" mid-13c., "an act of walking, a going on foot;" late 14c., "a stroll," also "a path, a walkway;" from walk (v.). The meaning "broad path in a garden" is from 1530s. Meaning "particular manner of walking" is from 1650s. Meaning "manner of action, way of living" is from 1580s; hence walk of life (1733). Meaning "range or sphere of activity" is from 1759. Sports sense of "base on balls" is recorded from 1905; to win in a walk (1854) is from horse racing (see walk-over). As a type of sponsored group trek as a fund-raising event, by 1971 (walk-a-thon is from 1963).

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pace (n.)

late 13c., "a step in walking," also "rate of motion; the space traveled by the foot in one completed movement in walking," from Old French pas "a step, pace, trace," and directly from Latin passus, passum "a step, pace, stride," noun use of past participle of pandere "to stretch (the leg), spread out," probably from PIE *pat-no-, nasalized variant form of root *pete- "to spread."

It also was, from late 14c., a lineal measurement of vague and variable extent, representing the space naturally traversed by the adult human foot in walking. In some places and situations it was reckoned as the distance from the place where either foot is taken up, in walking, to that where the same foot is set down again (a great pace), usually 5 feet or a little less. The pace of a single step (military pace) is about 2.5 feet.

To keep pace (with) "maintain the same speed, advance at an equal rate" is from 1580s. Pace-setter "one who establishes trends in fashion," is by 1895; it also had literal meanings.

It is customary for the contractor to employ some expert as a pace setter. A man who can thin an acre of beets a day commands as high as $2.00 per day as a pace setter. The other employees are paid in the proportion their work bears to that of the pace setter. The weak, lazy and unskillful get the smallest wage. Besides that the contractor runs a commissary department and feeds the gang. They sleep in tents or in the shade of trees near where they work. [report on Oxnard, Calif., beet harvesting in "The Louisiana Planter and Sugar Manufacturer," May 13, 1899] 
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andante (adj., n.)
musical direction, "moderately slow," 1742, from Italian andante, suggesting "walking," present participle of andare "to go," from Vulgar Latin ambitare (source of Spanish andar "to go"), from Latin ambitus, past participle of ambire "to go round, go about," from amb- "around" (from PIE root *ambhi- "around") + ire "go" (from PIE root *ei- "to go").
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digitigrade (adj.)
Origin and meaning of digitigrade

"walking on the toes with the heel raised from the ground" (opposed to plantigrade), by 1819, from Modern Latin digitigradus, from digitus "toe" (see digit) + gradi "to walk, go, step" (from PIE root *ghredh- "to walk, go"). As a noun, "a digitigrade mammal," by 1802.

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