A bottle support plate for use in a rotary capping machine used to apply caps onto the upper threaded neck of one or more containers having a non-fully circular flange. A generally C-shaped trocar provides increased work space between the hands of the surgeon as well as S-shaped laparoscopic instruments placed through the trocar when laparoscopic instrument-trocar units are placed through the umbilicus. An arbiter selects an appropriate arbitration configuration based on which units are active and which are stopped.