The method of the lower deformation energy has been successfully used for the synthesis of mechanisms for quite a while. It has shown to be a versatile, yet powerful method for assisting in the design of mechanisms. Until now, most of the implementations of this method used the dimensions of the mechanism as the synthesis variables, which has some advantages and some drawbacks. For example, the assembly configuration is not taken into account in the optimization process, and this means that the same initial configuration is used when computing the deformed positions in each synthesis point. This translates into a reduction of the total search space. A possible solution to this problem is the use of a set of initial coordinates as variables for the synthesis, which has been successfully applied to other methods. This also has some additional advantages, such as the fact that any generated mechanism can be assembled. Another advantage is that the fixed joint locations are also included in the optimization at no additional cost. But the change from dimensions to initial coordinates means a reformulation of the optimization problem when using derivatives if one wants them to be analytically derived. This paper tackles this reformulation, along with a proper comparison of the use of both alternatives using sequential quadratic programming methods. In order to do so, some examples are developed and studied.

翻译：低变形能方法在机构综合领域已成功应用相当长的时间，被证明是一种兼具通用性与有效性的机构设计辅助方法。目前该方法的多数实现均以机构尺寸作为综合变量，这种方法既有优势也存在不足。例如，优化过程未考虑装配构型，导致计算每个综合点处的变形位置时始终使用相同的初始构型，这相当于缩减了总搜索空间。解决该问题的一个可行方案是采用初始坐标集作为综合变量，该方法已成功应用于其他综合技术。该方案具有额外优势：首先，所生成的所有机构均可实现装配；其次，固定铰链位置无需增加额外成本即可纳入优化范畴。但将综合变量从尺寸替换为初始坐标意味着，若需解析推导优化问题的导数，则必须重新构建优化问题的数学表述。本文致力于解决这一重构问题，并基于序列二次规划方法对两种变量选取方案进行系统比较。为此，我们开发并研究了若干算例。