Happiness and Sorrow originates from the attachment of an object to the person who relates to it.To accept or renounce an object depends on the person's relationship to that object.The happiness in accepting the object, which a person experiences will not be there when the person renounces the object.This is because there is an inherent feeling that the object belongs to me.
There are 2 types of desires.One in which a person sacrifices something because he does not like it and another is where he accepts something because of liking. To Sacrifice something which a person does not like and the freedom experienced after that are the same.
Renunciation should be understood in a different way.When you sacrifice something which you don't like it cannot be called Renunciation.Renunciation is something which you like and sacrifice it for the benefit and prosperity of others.When you sacrifice something which gives you sorrow that does not mean it can give happiness to the person who accepted it.
Lets look at an example of a farmer who has got a cow which has got some disease.Normally what the farmer would do is to sell off the cow for whatever money he gets.The farmer does not even think that the difficulty he encountered with the sick cow is passed on to the person who buys it.Even if the farmer donates the cow by hiding the illness then also it cannot be called Renunciation as his action is involved with cheating and falsehood involved in hiding the disease of the cow.
Renunciation is sacrificing something which gave happiness and prosperity so that the person who accepts also enjoy the same level of happiness and prosperity.
The above points are taken from Padapooja book written by Jagadguru Swami Sathyananda Saraswathi Tiruvadikal .This book is an exhaustive text on the Guru -Shishya relation between BrahmaSree Neelakanta Gurupadar and Swamiji and the significance of the interactions of the Guru with the disciples and devotees.