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.
Highlights
Compared with traditional mechanisms with fixed mobility, reconfigurable mechanisms have variable numbers and types of mobility and a variety of configurations, which can meet the requirements for multi-tasks, multi-working conditions and multi-functions
We have revealed all the motion branches and singular configurations in the Schatz-inspired metamorphic mechanism as shown in Fig. 5, where I-III-II-IV-I correspond to configurations of the mechanism along motion branch 1 and I-V-II-VI-I correspond to configurations of the mechanism along motion branch 2
This paper established the high-order kinematic models of the Schatz-inspired metamorphic mechanisms and obtained velocity constraint equations and acceleration constraint equations using the sequential operation of the Lie bracket
Summary
Compared with traditional mechanisms with fixed mobility, reconfigurable mechanisms have variable numbers and types of mobility and a variety of configurations, which can meet the requirements for multi-tasks, multi-working conditions and multi-functions. We are going to reveal the bifurcation by establishing the high-order kinematic model and obtain the instantaneous joint velocities at the singular configuration of the mechanism, which can be obtained directly by the screw theory.
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