Abstract The revelation of mechanism bifurcation is essential in the design and analysis of reconfigurable mechanisms. The first- and second-order based methods have successfully revealed the bifurcation of mechanisms. However, they fail in the novel Schatz-inspired metamorphic mechanisms presented in this paper. Here, we present the third- and fourth-order based method for their bifurcation revelation using screw theory. Based on the constraint equations derived from the first- and second-order kinematics, only one linearly independent relationship between joint angular velocities at the singular configuration of the new mechanism can be generated, which means the bifurcation cannot be revealed in this way. Therefore, we calculate constraint equations from the third- and fourth-order kinematics, and attain two linearly independent relationships between joint angular accelerations at the same singular configuration that correspond to different curvatures of the kinematic curves of two motion branches in the configuration space. Moreover, motion branches in Schatz-inspired metamorphic mechanisms are demonstrated.

中文翻译：

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使用螺旋理论揭示新型 Schatz 启发变质机制的分岔的高阶基础

摘要 机构分岔的揭示对于可重构机构的设计和分析至关重要。基于一阶和二阶的方法已经成功地揭示了机制的分叉。然而，它们在本文提出的新颖的受沙茨启发的变质机制中失败了。在这里，我们使用螺旋理论提出了基于三阶和四阶的分岔揭示方法。基于由一阶和二阶运动学推导出的约束方程，新机构在奇异构型下的关节角速度之间只能产生一个线性无关的关系，这意味着不能以这种方式揭示分岔。因此，我们从三阶和四阶运动学计算约束方程，并在同一奇异配置下获得两个线性无关的关节角加速度关系，它们对应于配置空间中两个运动分支的运动学曲线的不同曲率。此外，还展示了受 Schatz 启发的变形机制中的运动分支。