This paper presents the formulation of a reduced-order linear discrete–path approximation in state space and its solution as a function of path lengths for a 3D curvature-based beam model (CBM). Solutions to both forward and inverse problems are discussed; the former is essential for real-time deformed shape visualization whereas the latter is much needed for haptic force feedback. The method is illustrated with an application example where a 2D beam is characterized by a 6th order CBM. Practical implementation shows that when external forces as system input are expressed in global coordinates, the CBM can be decoupled into two 2nd order systems enabling parallel computing of the deformed shape and the orientation and moment, and effectively reducing the table size for storing the operating conditions. The proposed real-time computation method has been validated by verifying results against published experimental and MSM simulated data.
- Dynamic Systems and Control Division
Discrete Deformation Models for Real-Time Computation of Compliant Mechanisms
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Ji, J, & Lee, K. "Discrete Deformation Models for Real-Time Computation of Compliant Mechanisms." Proceedings of the ASME 2013 Dynamic Systems and Control Conference. Volume 3: Nonlinear Estimation and Control; Optimization and Optimal Control; Piezoelectric Actuation and Nanoscale Control; Robotics and Manipulators; Sensing; System Identification (Estimation for Automotive Applications, Modeling, Therapeutic Control in Bio-Systems); Variable Structure/Sliding-Mode Control; Vehicles and Human Robotics; Vehicle Dynamics and Control; Vehicle Path Planning and Collision Avoidance; Vibrational and Mechanical Systems; Wind Energy Systems and Control. Palo Alto, California, USA. October 21–23, 2013. V003T39A006. ASME. https://doi.org/10.1115/DSCC2013-4108
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