Over the course of history, the alignment of the U.S. Democratic and Republican parties with the "political right" and "political left" has changed. For example, the Republican Party from the Civil War to the Progressive Era could be labelled on the political left; yet today that party is on the political right.
Seating in the United States Senate and House chambers is also divided between the left side and the right side. Currently, Democrats sit in the seats to the presiding officer's right, and Republicans sit to the left. (In contrast, the ruling party of the U.K. House of Commons always sits to the right, and the opposition party always sits on the left; a change in the ruling party switches which party is on the right side of the chamber.)
Has the realignment of a party's political philosophy ever resulted in a reversal of their seating in either chamber of Congress? In other words, has any political party ever literally "switched sides" in Congress?