Abstract
This thesis presents a method-comparison study to evaluate the applicability and the effectiveness of the instant center approach, compared with the conventional envelope theory. Given the same input parameters, two methods yield identical resulting envelopes, which are illustrated analytically and numerically via the case studies. The main aim of this thesis is illustrating the merits of adopting the instant-center approach over the envelope theory. The formulation based on the envelope theory is purely an algebraic arrangement. Expressing an envelope in an explicit form involve differentiation and simultaneous solution of equations describing a family of straight lines, which are burdensome and difficult to operate. Oppositely, using the concept of instant center allows one to locate the common normal which pass through the instant center and at last determine the envelope. This approach offers more intuitive comprehensions about geometric features of a mechanism of interest, comparably simple and efficient. The case studies also have shown an insightfully geometric fact that a second family of straight lines is a straight trajectory orthogonal to a family of straight lines.