The humorous expression elbow grease denotes vigorous physical labour, especially hard rubbing.

This expression is first recorded in Paroemiologia Anglo-Latina In usum Scholarum concinnata. Or Proverbs English, and Latine, methodically disposed according to the Common-place heads, in Erasmus his Adages (London: Imprinted by Felix Kyngston for Robert Mylbourne […], 1639), by John Clarke (1596?-1658):

Earely to bed and earely to rise, makes a man healthy, wealthy, and wise.
By line and levell.
Use the means and trust God for a blessing.
It smells of elbow-grease.
Help thy self, and God will help thee.

In Clarke’s book, “it smells of elbow-grease” translates the Latin phrase olet lucernam, literally it smells of the lamp, referring to nocturnal study by lamplight—cf. to burn the midnight oil.

The expression elbow grease then occurs in Gregory, Father-Greybeard, With his Vizard off: Or, News from the Cabal In some Reflexions Upon a late Pamphlet Entituled, The Rehearsal Transpros’d. (After the fashion that now obtains) In a Letter to our old Friend, R. L. from E. H. (London: Printed by Robin Hood […], And sold by Nath. Brooke […], 1673), by Edmund Hickeringill (1631-1708):

Oh Hudibras! Droll Laureat! Wits-Common-wealth! or which is more, friend to Trans! Poor wit might have slept quietly, (as she has done time out of mind,) but that Hud took her napping, gave her a twitch by the nose, and made her wait on him in the shape of a Droll, draws a Circle and conjured her, henceforward never so much as to look at a Cassock, a Quoif, a Gown, or a Bulls-cap; but by no means on a Black-Cap white-fac’d, nor so much as to come within sight of the Cradle upon Kings-Colledge-Chappel, but be confin’d henceforth for ever to the Coffee-house, Clubs, Drolls, Virtuoso’s, and Ingenioso’s; who now, with the help of the Press, Coffee, and the Wine-Press, want nothing but Ink and Elbow-grease, (as Trans threatens the trembling world,) to do more harm than an hundred Systematical Divines, with their sweaty Preaching.
[…]
What think you friends; I only propose it; what think you of making another Gathering among the Churches for our friend—The Author of The Rehearsal Transpros’d, to chear up his drooping spirits, for I hear he is crop-sick, and his spirit, like Nabal’s, almost dead within him; but a little encouragement from you, I only give you my thoughts, would perhaps make him still get some more Ink and Elbow griese, and spend it briskly once more in behalf of modern Orthodoxy, and the Good Old Cause.

The expression elbow grease was recorded in A New Dictionary of the Terms Ancient and Modern of the Canting Crew. In its several Tribes, of Gypsies, Beggers, Thieves, Cheats, &c. With an Addition of some Proverbs, Phrases, Figurative Speeches, &c. Useful for all sorts of People, (especially Foreigners) to secure their Money and preserve their Lives; besides very Diverting and Entertaining, being wholly New (London: Printed for W. Hawes […], P. Gilbourne […], and W. Davies […] – [1699]), by “B. E. Gent.”:

Elbow-grease, a derisory Term for Sweat. It will cost nothing but a little Elbow-grease; in a jeer to one that is lazy, and thinks much of his Labour.

FRENCH: HUILE DE COUDE

The corresponding French expression is huile de coude, literally elbow oil.

The earliest occurrence of huile de coude that I have found is from Dictionnaire universel de commerce, d’histoire naturelle, & des arts & métiers (Copenhagen: Cl. & Ant. Philibert, 1761), by Jacques Savary des Brûlons (1657-1716) and his brother, Philémon-Louis Savary:

Si l’on observe tout ce que nous venons de dire, qu’on ait employé de l’acier bien choisi, on pourra se flatter d’avoir fabriqué une bonne piéce, à laquelle il ne manquera plus que de donner à coups de Marteau la forme qu’on désire, ce qui se fait en la chaufant & forgeant au point requis ; & si l’on y procéde réguliérement, il y aura peu à travailler avec la lime, qui ne sera néessaire [sic] que pour adoucir & lui donner plûtôt la bonne grace que l’utilité : on demande pourtant l’un & l’autre, ainsi l’on n’épargnera pas ce que l’Ouvrier appelle l’huile de coude.
     translation:
If one observes all we have just said, if one has employed well-chosen steel, one will be able to flatter oneself for having made a good device, to which one will only have to give, with hammer blows, the shape that one desires, which is done by heating and forging it to the requested point; and if one carries this out steadily, there will be little to file off, which will only be necessary to soften and give it good grace rather than usefulness: yet both are required, so one will not spare oneself what the workman calls elbow oil.

The second-earliest occurrence of huile de coude that I have found is from Voyage bibliographique, archéologique et pittoresque en France (Paris: Chez Crapelet, imprimeur-éditeur, 1825)—translated by Théodore Licquet (1787-1832) from A Bibliographical, Antiquarian and Picturesque Tour in France and Germany (London: Printed for the author, by W. Bulmer and W. Nicol, 1821), by the British bibliographer Thomas Frognall Dibdin (1776-1847):

Sous le rapport de l’ameublement, je dois aux Rouennais la justice d’avouer que je n’ai jamais rien vu de comparable à leurs escritoires et autres meubles en noyer. Il y a de ces hautes escritoires, ou secrétaires, dans presque toutes les chambres à coucher des principaux hôtels ; mais une fois déposés à demeure dans l’auberge, ils perdent leur poli, attendu que l’art du frotteur, ou ce que nous appelons chez nous elbow-grease (a), est pour ainsi dire inconnu sur les deux rives de la Seine.
(a) Littéralement, huile de coude, pour exprimer un travail rude.

Original text by Thomas Frognall Dibdin:

In respect to upholstery, I must do the Rouennois the justice to say, that I never saw any thing to compare with their escrutoires and other articles of furniture made of the walnut tree. These upright escrutoires, or writing desks, are in almost every bed-room of the more respectable hotels: but of course their polish is gone when they become stationary furniture in an inn—for the art of rubbing, or what is called elbow-grease with us, is almost unknown on either side of the Seine.

An earlier French expression, graisse de bras, literally arm grease, occurs in Traité de la Prudence, contenant un grand nombre d’Instructions, de Sentences, & de Proverbes choisis (Besançon, 1733), by Antoine Dumont, pseudonym of Jean-Baptiste Arnoult (1689-1753):

Travaillés & aimés le travail, soïés laborieux ; quand on veut aspirer aux grandes choses, on ne doit pas se delicater, chercher trop ses aises & vivre dans la molesse & la volupté, mais s’acoûtumer à la peine, à la fatigue & aux veilles. Les Armuriers font reluire, briller leurs ouvrages avec de la graisse de bras C. ils les polissent en les frotant de toutes leurs fotces [sic], voilà votre modéle.
     translation:
Work and love work, be industrious; when one wants to aspire to great things, one must not become sluggish, nor excessively seek creature comforts, nor live in indolence and sensual pleasure, but [one must] accustom oneself to effort, to tiredness and to sleepless nights. Armourers make their artefacts gleam, shine with arm grease, that is to say, they polish them by rubbing them as hard as they can, that is the model for you to follow.