One widely-used scissor lift mechanism with the input mode of single hydraulic cylinder is researched. A unified accurate mechanics model of mechanism arms is constructed. By establishing statics, interior forces and stress formula, the general strength optimization design method of arms is explored. Through analysis of an existed sample, validity of the proposed method is verified in contrast with experiment results. Variation law of mechanical parameters within lifting process is uncovered by modeling analysis of the sample mechanism, which also indicated the necessacity of arms optimization. Finally, a dimension optimization of box arms of proposed mechanism is fulfilled with concept of constant strength to prepare for the coming finite element simulation, experiment research.