A Substructure Condensed Approach for Kinetostatic Modeling of Compliant Mechanisms with Complex Topology

Area of Science:

• Mechanical Engineering
• Robotics
• Precision Engineering

Background:

• Compliant mechanisms offer high precision and compact designs for advanced devices.
• Complex topologies in these mechanisms present analytical challenges.

Purpose of the Study:

• To propose a substructure condensed approach for efficient kinetostatic analysis of complex compliant mechanisms.
• To develop a concise modeling method for precision devices with intricate compliant structures.

Main Methods:

• Derived explicit relationships for stiffness and transfer matrices of flexible beam elements using energy conservation.
• Developed transfer matrices for serial-parallel substructures by combining equilibrium equations and transfer matrix methods.
• Established a kinetostatic model focusing on input/output force-displacement relationships.

Main Results:

• Successfully condensed complex compliant mechanism branches into equivalent beam elements.
• Created a kinetostatic model yielding explicit matrix forms for stiffness and displacement.
• Demonstrated the approach's conciseness and efficiency on precision positioning platforms.

Conclusions:

• The substructure condensed approach provides a distinct and effective alternative to traditional compliance matrix methods.
• This method simultaneously obtains input/output stiffness, coupling stiffness, and displacement relations for complex compliant mechanisms.