The purpose of this paper is to develop a new approach to evolutionary synthesis for applications involved in the design of collision-free linkage mechanisms. We first analyze the kinematical position, velocity, and acceleration equations for mechanisms in question and utilize the inferred equations to formulate practical collision-free requirements into geometrical constraints and convert manufacturing criteria into multiple objectives. In order to explore precise and widespread design solutions, we develop an improved version of the method of inequality-based multiobjective genetic algorithms (MMGA) by employing a Euclidean-distance-based diversity method, to serve as a global explorer. Several case studies are used to verify the correctness and effectiveness of the proposed approach, and the results have been successfully applied to the design of a commercial-use ladle mechanism, which has been hindered by obstacles from related peripheral equipment.