Yevamos 39b: Abba Shaul says: One who marries his brother’s wife for the sake of her beauty, for the sake of marital relations, or for some other ulterior motive, is considered as if he is having an immoral relationship.
Rema, Even Hoezer 165:1: Even if both of them wish to do yibum, we do not allow them, unless it is obvious that they intend to do it for the sake of the mitzvah.
יבמות לט ע”ב: אבא שאול אומר: הכונס את יבמתו לשם נוי, ולשום אישות, ולשום דבר אחר ־ כאילו פוגע בערוה, וקרוב אני בעיני להיות הולד ממזרֹ וחכמים אומרים: (דברים כ״ה) יבמה יבא עליה ־ מכל מקום.
אה”ע קס”ה ס”א רמ”א: ואם שניהם רוצים ביבום אין מניחים אותם לייבם אא״כ ניכר וידוע שמכוונים לשם מצוה (טור בשם ר״ת).
רמב”ם יבום וחליצה ד,יז: יבם שרגלו הימנית חתוכה אינו חולץ בשמאל ואם חלצה מעל שמאלו חליצתה פסולה , היתה רגלו עקומה לאחור או הפוכה על צידה או שהיה מהלך על ראשי אצבעות רגליו הרי זה אינו חולץ שהחולץ צריך לנעוץ עקיבו בארץ וזה אינו יכול ואם חלצה למי שרגלו כך חליצתה פסולה.
אה”ע קסט,לד: היתה רגלו עקומה לאחור או הפוכה על צדה או שמהלך על אצבעות רגליו אינו חולץ:
Yisroel Chaim and his wife Chaya lived in Jerusalem, and had no children. When Yisroel Chaim passed away in 1925 at the age of 35, the Beis Din asked Chaya, “Did your husband have any brothers?” “Yes,” she said, “he had one brother living in New York.” The Beis Din in Jerusalem wrote to a rav in New York, asking if he could locate the brother and help arrange a chalitzah.
The rav in New York managed to locate the brother. As the brother came into the rav’s house, the rav noticed that he was limping on his right foot. “Can you please take off your shoes and socks?” said the rav. The man did as he was told; the rav saw that his whole foot was bent backward, and he was walking on two of his toes. In such a case, the Rambam (Yibum Vachalitzah 4:17) and the Shulchan Aruch (Even Hoezer 169:34) rule that one cannot do chalitzah. And Ashkenazim, following the position of Abba Shaul, do not practice yibum nowadays. But then what was the solution for the poor widow? Was she to remain single for life?
The rav sent the question to Rabbi Chaim Ozer Grodzensky in Vilna, who replied, “The poskim such as the Shvus Yaakov, Knesses Yechezkel and the Beis Meir permit yibum even today in such situations. Even if the brother is already married, he may marry the widow; Rabbeinu Gershom’s ban on polygamy does not apply in this case. Furthermore, after marrying her, he may divorce her immediately, even without her consent. This is all cited as practical halacha by the Pischei Teshuva, Even Hoezer 165:3.”
Although the Shav Yaakov disagreed, invoking the rule that “anyone who cannot do chalitzah, cannot do yibum,” the other poskim argued that this rule does not apply when the chalitzah can’t be done for purely physical reasons. Reb Chaim Ozer adds that the Ritva in Chullin 92 says this explicitly. Therefore, the best solution for this case was that the brother in New York should marry his deceased brother’s wife.
However, if that was impossible, Reb Chaim Ozer said that if the man was able to push his right heel into the ground, even painfully, they could rely on a combination of two lenient opinions and do chalitzah with the right foot, and then again with the left foot (because perhaps in a case like this, the man learns to favor his left foot and he has the status of a lefty, who can do chalitzah according to some Rishonim).
Source: Achiezer 3:20
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