This thesis study focuses on coupler-curve of planar slider-crank and four-bar mechanisms. The geometric properties of the coupler-curve equations are investigated. The coupler-curve equations of both slider-crank and four bar mechanisms are shown to consist of quadratic and linear components. The quadratic components that appear in the coupler-curve equations are circles which determine the area the coupler-curve may be located. The path generation problem of the slider-crank mechanism is another aspect of this thesis. A limited solution to the path generation problem is introduced and tested numerically. A method that is a combination of the discovered geometric properties of the coupler-curve and numerical approximation methods is introduced. The solution approach works for the task of fitting a coupler-curve on a cluster of points and five precision points problem.