A computer-based algorithm to enumerate the locations of instantaneous centres of planar mechanisms is developed. There exists a matrix method of obtaining instantaneous centres of planar mechanisms implementing Kennedy's theorem into a matrix form, but it has such limitations that many classes of planar mechanisms cannot be handled properly. The algorithm proposed here is basically an extension of the matrix method to handle any kind of planar mechanism. Several classes of planar mechanism are studied by these two methods to demonstrate the differences between them.