The effect of frequency and clearance variations on single-degree-of-freedom impact oscillators

1995 ◽  
Vol 184 (3) ◽  
pp. 475-502 ◽  
Author(s):  
C. Budd ◽  
F. Dux ◽  
A. Cliffe
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Impact Oscillators ◽  
Single Degree

Co-dimension-Two Grazing Bifurcations in Single-Degree-of-Freedom Impact Oscillators

2006 ◽  
Vol 1 (4) ◽  
pp. 328-335 ◽  
Author(s):  
Phanikrishna Thota ◽  
Xiaopeng Zhao ◽  
Harry Dankowicz
Keyword(s):  
Degree Of Freedom ◽  
Mapping Technique ◽  
Global Dynamics ◽  
Grazing Bifurcation ◽  
Single Degree Of Freedom ◽  
Bifurcation Points ◽  
Impact Oscillators ◽  
Single Degree ◽  
Dimension One ◽  
Grazing Bifurcations

Grazing bifurcations in impact oscillators characterize the transition in asymptotic dynamics between impacting and nonimpacting motions. Several different grazing bifurcation scenarios under variations of a single system parameter have been previously documented in the literature. In the present paper, the transition between two characteristically different co-dimension-one grazing bifurcation scenarios is found to be associated with the presence of certain co-dimension-two grazing bifurcation points and their unfolding in parameter space. The analysis investigates the distribution of such degenerate bifurcation points along the grazing bifurcation manifold in examples of single-degree-of-freedom oscillators. Unfoldings obtained with the discontinuity-mapping technique are used to explore the possible influence on the global dynamics of the smooth co-dimension-one bifurcations of the impacting dynamics that emanate from such co-dimension-two points. It is shown that attracting impacting motion may result from parameter variations through a co-dimension-two grazing bifurcation of an initially unstable limit cycle in a nonlinear micro-electro-mechanical systems (MEMS) oscillator.

Kinematic comparison of single degree-of-freedom robotic gait trainers

2021 ◽  
Vol 159 ◽  
pp. 104258
Author(s):  
Jeonghwan Lee ◽  
Lailu Li ◽  
Sung Yul Shin ◽  
Ashish D. Deshpande ◽  
James Sulzer
Keyword(s):  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Robotic Gait
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