May one cry on Shabbos?

One who receives pleasure from crying, may cry on Shabbos.[1] Thus, one may cry out of feelings of yearning and Dveikus for Hashem, such as occurs by those who Daven with concentration.[2] Furthermore, if one is saddened by a certain matter, and by crying over the matter it will release the pain, then it is permitted to cry on Shabbos.[3] 

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[1] Rama 288:2; Iggur in name of Shibulei Haleket; Midrash brought in Taz 288:1 that the students of Rebbe Akiva once found him crying on Shabbos and asked him why he is crying and he answered that it is a pleasure for him to cry. Vetzaruch Iyun as to why this ruling was omitted by Admur

[2] Taz 288:2 that the crying of Rebbe Akiva was done out of pleasure of Dveikus to Hashem, as stated in the Zohar that Rebbe Akliva would tear while reading Shir Hashirim

[3] Rama ibid; Elya Raba 288:3; Tosefes Shabbos 288:3; Mateh Yehuda 288:10; P”M 288 M”Z 2; Aruch Hashulchan 288:6; M”B 288:4; Kaf Hachaim 288:9; Piskeiy Teshuvos 288:2

The source: As it states in the Midrash and Yerushalmi that Rebbe Akiva was crying due to sadness, due to the passing of his son. [Tosefes Shabbos ibid]

Other opinions: Some Poskim rule it is forbidden to cry out of sadness on Shabbos, even if one desires to do so in order to release the pain. [Taz ibid]

[4] Rama ibid; Elya Raba 288:3; Tosefes Shabbos 288:3; Mateh Yehuda 288:10; P”M 288 M”Z 2; Aruch Hashulchan 288:6; M”B 288:4; Kaf Hachaim 288:9; Piskeiy Teshuvos 288:2

The source: As it states in the Midrash and Yerushalmi that Rebbe Akiva was crying due to sadness, due to the passing of his son. [Tosefes Shabbos ibid]

Other opinions: Some Poskim rule it is forbidden to cry out of sadness on Shabbos, even if one desires to do so in order to release the pain. [Taz ibid]

[5] Amudei Or 76, brought in Kaf Hachaim 288:10