Probabilistic Elastic Element Design for Robust Natural Dynamics of Structure-Controlled Variable Stiffness Actuators

2017 ◽  
Vol 10 (1) ◽  
Author(s):  
Florian Stuhlenmiller ◽  
Jochen Schuy ◽  
Philipp Beckerle
Keyword(s):  
Elastic Element ◽  
Material Selection ◽  
Probabilistic Approach ◽  
Design Procedure ◽  
Variable Stiffness ◽  
Actuation System ◽  
Lumped Parameter ◽  
Stiffness Properties ◽  
Natural Dynamics ◽  
Variable Stiffness Actuators

This paper proposes a probabilistic approach for the design of elastic elements to be used in structure-controlled variable stiffness actuators (VSA) for robotic applications. Considering the natural dynamics of the elastic actuation system, requirements are defined and material selection as well as geometry calculation are performed using lumped parameter models. Monte Carlo simulations are integrated in the design procedure to ensure a robust implementation of the required dynamical characteristics. Thereby, effects of uncertainties that might be caused by manufacturing or deviations of material properties are taken into account. To validate the suitability of the overall approach and the particular methods, a torsional elastic element is implemented and experimentally evaluated. The evaluation shows a fulfillment of the key requirements, i.e., specific natural dynamic behavior, that is only achieved due to considering uncertainties. Further, the transferability of the approach to other structure-controlled elastic actuators is discussed and implications are given. Only the governing equations of stiffness properties in certain load situation need to be adapted, e.g., from torsion to bending. Due to the simple transfer, the proposed probabilistic and model-based approach is promising for application to various actuator concepts with structure-controlled variable stiffness.

scholarly journals Design of External Rotor Ferrite-Assisted Synchronous Reluctance Motor for High Power Density

2021 ◽  
Vol 11 (7) ◽  
pp. 3102
Author(s):  
Md. Zakirul Islam ◽  
Seungdeog Choi ◽  
Malik E. Elbuluk ◽  
Sai Sudheer Reddy Bonthu ◽  
Akm Arafat ◽  
...  
Keyword(s):  
Rare Earth ◽  
Permanent Magnets ◽  
Design Procedure ◽  
Lumped Parameter Model ◽  
High Power Density ◽  
Analytical Design ◽  
Synchronous Reluctance Motor ◽  
Lumped Parameter ◽  
Reluctance Motor ◽  
External Rotor

The rare-earth (RE) permanent magnets (PM) have been increasingly adopted in traction motor application. However, the RE PM is expensive, less abundant, and has cost uncertainties due to limited market suppliers. This paper presents a new design of a RE-free five-phase ferrite permanent magnet-assisted synchronous reluctance motor (Fe-PMaSynRM) with the external rotor architecture with a high saliency ratio. In such architecture, the low magnetic coercivity and demagnetization risk of the ferrite PM is the challenge. This limits the number of flux barriers, saliency ratio, and reluctance torque. A precise analytical design procedure of rotor and stator configuration is presented with differential evolution numerical optimizations by utilizing a lumped parameter model. A 3.7 kW prototype is fabricated to validate the proposed idea.

Design Nomographs of Compression Helical Springs for Predetermined Reliability Levels

1981 ◽  
Vol 103 (2) ◽  
pp. 268-273
Author(s):  
My Dao Thien ◽  
M. Massoud
Keyword(s):  
Probabilistic Approach ◽  
Design Procedure ◽  
Axial Loading ◽  
Geometric Parameters ◽  
Computer Algorithms ◽  
Mean Values ◽  
Helical Springs ◽  
Reliability Level ◽  
Classical Design ◽  
Mission Success

This paper discusses a probabilistic approach for the design of Compression Closely Coiled Helical Springs subjected to periodic axial loading. The classical design procedure results in deterministic geometric parameters with tolerances normally chosen according to standards without due regard to their effects on the mission success as normally expressed by a reliability level. With the proposed design procedure, the engineer can specify nominal mean values for the geometric parameters and their tolerances according to a predetermined reliability level. Design nomographs are presented to help the engineer, in the early stages of design, to choose between many alternatives. Computer algorithms can easily be written to verify the final or optimum design.

scholarly journals A reduced order computational model of a semi-active variable-stiffness foot prosthesis

2020 ◽  
Author(s):  
Michael McGeehan ◽  
Peter Adamczyk ◽  
Kieran Nichols ◽  
Michael Hahn
Keyword(s):  
Body Weight ◽  
Center Of Pressure ◽  
Reaction Force ◽  
Variable Stiffness ◽  
Performance Standard ◽  
Design Parameters ◽  
Compression Tests ◽  
Static Compression ◽  
Lumped Parameter ◽  
Contact Models

INTRODUCTION: Passive energy storage and return (ESR) feet are the current performance standard in lower limb prostheses. A recently developed semi-active variable-stiffness foot (VSF) prosthesis balances the simplicity of a passive ESR device with the adaptability of a powered design. The purpose of this study was to model and simulate the ESR properties of the VSF prosthesis. METHODS: The ESR properties of the VSF were modeled as a lumped parameter overhung beam. The overhung length is variable, allowing the model to exhibit variable ESR stiffness. Foot-ground contact was modeled using sphere-to-plane contact models. Contact parameters were optimized to represent the geometry and dynamics of the VSF and its foam base. Static compression tests and gait were simulated. Simulation outcomes were compared to corresponding experimental data. RESULTS: Stiffness of the model matched that of the physical VSF (R2: 0.98, RMSE: 1.37 N/mm). Model-predicted resultant ground reaction force (GRFR) matched well under optimized parameter conditions (R2: 0.98, RMSE: 5.3% body weight,) and unoptimized parameter conditions (R2: 0.90, mean RMSE: 13% body weight). Anterior-posterior center of pressure matched well with R2 > 0.94 and RMSE < 9.5% foot length in all conditions. CONCLUSIONS: The ESR properties of the VSF were accurately simulated under benchtop testing and dynamic gait conditions. These methods may be useful for predicting GRFR arising from gait with novel prostheses. Such data are useful to optimize prosthesis design parameters on a user-specific basis.

scholarly journals Classification of Variable Stiffness Actuators - part 2

2017 ◽  
Vol 21 (2) ◽  
pp. 15-23
Author(s):  
Bartłomiej Kozakiewicz ◽  
Tomasz Winiarski
Keyword(s):  
Variable Stiffness ◽  
Variable Stiffness Actuators

scholarly journals Robust tracking control for two classes of variable stiffness actuators based on linear extended state observer with estimation error compensation

2020 ◽  
Vol 17 (2) ◽  
pp. 172988142091177
Author(s):  
Jishu Guo ◽  
Junmei Guo ◽  
Zhongjun Xiao
Keyword(s):  
Linear System ◽  
Tracking Control ◽  
Estimation Error ◽  
Input Saturation ◽  
Variable Stiffness ◽  
State Observer ◽  
Extended State Observer ◽  
Extended State ◽  
Linear Extended State Observer ◽  
Variable Stiffness Actuators

In this article, a novel robust tracking control scheme based on linear extended state observer with estimation error compensation is proposed for the tracking control of the antagonistic variable stiffness actuator based on equivalent nonlinear torsion spring and the serial variable stiffness actuator based on lever mechanism. For the dynamic models of these two classes of variable stiffness actuators, considering the parametric uncertainties, the unknown friction torques acting on the driving units, the unknown external disturbances acting on the output links and the input saturation constraints, an integral chain pseudo-linear system with input saturation constraints and matched lumped disturbances is established by coordinate transformation. Subsequently, the matched lumped disturbances in the pseudo-linear system are extended to the new system states, and we obtain an extended integral chain pseudo-linear system. Then, we design the linear extended state observer to estimate the unknown states of the extended pseudo-linear system. Considering the input saturation constraints in the extended pseudo-linear system and the estimation errors of the linear extended state observer with fixed preset observation gains, the adaptive input saturation compensation laws and the novel estimation error compensators are designed. Finally, a robust tracking controller based on linear extended state observer, sliding mode control, adaptive input saturation compensation laws, and estimating error compensators is designed to achieve simultaneous position and stiffness tracking control of these two classes of variable stiffness actuators. Under the action of the designed controller, the semi-global uniformly ultimately bounded stability of the closed-loop system is proved by the stability analysis of the candidate Lyapunov function. The simulation results show the effectiveness, robustness, and adaptability of the designed controller in the tracking control of these two classes of variable stiffness actuators. Furthermore, the simulation comparisons show the effectiveness of the proposed estimation error compensation measures in reducing the tracking errors and improving the disturbance rejection performance of the controller.

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