I have one similar to the bike you have pictured. it is a 79 to 86 KZ model. it could of had a 650 i4 a 750 i4 or a 400 twin or a 750 twin it could also have been a kz1000. but its definatley a KZ model and that will help alot for you. is there a metal tag stamped to the neck on the left side of the bike? If it is that will help you tremendously.