There are infinite number of Grash of mechanism solutions present in Burmester curve to attain the number of predefined coupler positions. By providing some constraints namely extremity of transmission angle, Grash of conditions and minimum perimeter condition or compactness condition. A synthesized mechanism can be obtained from these solutions, whose coupler point passes through predefined points. In this work an aeroplane landing gear mechanism is designed by the help of compactness algorithm in which Filemon’s construction is also applied to already defined constraints for getting a defect free synthesized mechanism. A defect free mechanism will attain or approximate all the prescribed precision positions by path generator. In this work path generator is produced by taking four precision positions points. This work proposes an algorithm named as compactness algorithm and one application to verify. Algorithm is codified in MATLAB due to its vectorised operation in less time.