Rica ederim emine nur

Rica ederim emine nur

U should understand that you are actually using a noun here: söyleme.

Where in English you say ´I want you to sing´ in Turkish you actually say ´I want your singing´.

Here is some explanation: http://www.turkishlanguage.co.uk/infinitive.htm 

In yapmasını the construction is

-ma = verb to noun (mak - k), -ing

-sı = his

-n = connection ´n´

ı = object condition/accusative

Yapmasını litterally means ´his/her making´ but we translate it as ´him/her to make´.