R Yehoshua Neuwirth in Shemirath Shabbath Kehilchata (vol. 1, p. 158) is strict
One should not, as a rule, perform physical exercises on Shabbat or Yom Tov, whether with or without the use of an instrument designed for strengthening muscles, such as a chest-expander. Likewise, one should not engage in occupational therapy.
He then makes exemptions for exercises required for one's health (and recommends to ask a Rav) or for simple, light exercises with one's hand.
R Ari Enkin here writes "Exercising or any other bodily exertion is generally forbidden on Shabbat" and further quotes the Mishna Brura 301.7