This is Sunnah (Way of Prophet Muhammad (May Allah honour Him and grant Him peace))for men but not for women during the Tawaaf of arrival (Tawaaf al-qudoom), which is the first Tawaaf performed when one arrives in Makkah.
It is only prescribed to uncover the right shoulder and walk quickly with short steps (raml) in the Tawaaf of ‘Umrah, and in the Tawaaf of arrival (Tawaaf al-qudoom) for those who are doing ifraad and qiraan Hajj. In other Tawaafs these actions are not prescribed, so in Tawaaf al-ifaadah there is no raml and no uncovering the shoulder, whether you did Tawaaf in Ihram or not. .
The male pilgrim covers the first three rounds of Tawaaf at a brisk pace, up to the Yemeni Corner. This is called ‘Raml’. The stretch from the Yemeni Corner to the Black Stone must be done at normal pace. The rest of the rounds and the seven rounds of female pilgrims are also done at the usual pace. Sahih Al-Bukhari 672
Uncovering the right shoulder and walking quickly with short steps (raml) go together. When raml is prescribed, uncovering the right shoulder is also prescribed; when raml is not prescribed, uncovering the shoulder is not prescribed either.
Narrated in Sahihain from Ibn Abbas (R) said: The Messenger of Allah (May Allah honour Him and grant Him peace) came with his companions and the mushrikoon said, “There have come to you people who have been weakened by the fever of Yathrib. So the Prophet Muhammad (May Allah honour Him and grant Him peace) commanded them to walk quickly (raml) in the first three circuits… According to another report, he said, “Walk quickly so that the mushrikeen will see that you are strong.” Sahih Al Bukhari Vol 2:469-470, 1602(NE) and Sahih Al Muslim Vol 2: 991-992, 1262(NE)
Ibn ‘Abbas (R) said that the Prophet Muhammad (May Allah honour Him and grant Him peace) did not walk quickly in the seven circuits of Tawaaf al-ifaadah. This was classed as saheeh by al-Albaani in Sahih Abu Dawood, Abu Dawood 2001.
The Messenger (May Allah honour Him and grant Him peace) uncovered one of his shoulders through his top garment then said: ‘Do not let the people see you as deficient/weak.’‘Ibn ‘Abbas(R) informed me that the Prophet (May Allah honour Him and grant Him peace)did this in his farewell Hajj.’
But Raml and uncovering the shoulder are separate in one case, which is that uncovering the shoulder is Sunnah in all seven circuits, but Raml is only Sunnah in the first three circuits, and one should walk (normally) in the last four.
Its chain is also authentic according to the conditions of Imam Muslim. It was also narrated by al-Bayhaqi in his book ‘Dala’il an-Naboowa’ (3/3/1) through two routes. Muslim narrated it (4/64) by way of al-Jareeri on the authority of Abu Tufail with a similar narration and it has been researched in ‘al-Irwaa’ (4/315).
It is Sunnah to uncover the right shoulder in all circuits of the Tawaaf of arrival only, and it is prescribed to walk quickly in the first three circuits of the Tawaaf of arrival for those doing Hajj and those doing ‘Umrah.
Shaykh Ibn Baaz (May Allah have mercy on him) said: He should walk quickly (raml) in the first three circuits of the first Tawaaf, which is the Tawaaf he performs when he first arrives in Makkah, whether he is doing ‘Umrah or Hajj Tamattu’, or he has entered Ihram for Hajj only, or is combining Hajj and ‘Umrah (Qiran). And he should walk in the last four circuits, starting each circuit with rapid steps. And it is mustahabb for him to uncover his right shoulder throughout this Tawaaf, but not in others, Fataawa Ibn Baaz, 16/60.