Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.076B.

Ramal means walking fast, vigorously moving the shoulders and taking small steps, giving a sense of strength and energy. Ibn ‘Umar reported that Allah’s Messenger (peace be upon him) jogged from the Black Stone to the Black Stone three times, and walked the remaining four rounds. (Muslim and Ahmad) If a person does not jog in the first three rounds, then he is not required to make it up in the last four rounds. Ramal (Jogging) and idtiba’ (uncovering one’s right shoulder) are prescribed for men only while making tawaffor ‘Umrah. In case of a pilgrim performing Hajj, tawaf is always followed by Sa’i (walking between Safa and Marwah). Shafi’i school holds that a pilgrim, who does make idtiba’ (i.e., uncovers his right shoulder) and performs ramal (i.e., jogs), while making Tawaf al Qudum on arrival and then making Sa’i between Safa and Marwah, is not required to repeat idtiba’ and ramal in his Tawaf al Ifada (after returning from ‘Arafah). If one does not perform Sa’i after making tawaf and postpones it till after Tawaf az-Ziarah (Tawaf of Visit), he should make idtiba’ (uncover his right shoulder) and perform ramal (jog) while making Tawaf az-Ziarah.

Women are not obligated to jog or uncover their right shoulder, because they must properly cover themselves. Ibn ‘Umar said: -Women are not obligated to jog around the Ka’bah nor while making Sa`i between Safa and Marwah.” (Reported by Al-Baihaqi)