Conformational analysis of stiff chiral polymers with end-constraints

Kim, Jin Seob; Chirikjian, Gregory S.

doi:10.1080/08927020601024137

Cited by 36 publications

(46 citation statements)

References 61 publications

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“…A roving hammer method is used to excite, in the x direction, the two sides of the band (i.e.. Points 1-6 and Points [14][15][16][17][18][19][20][21][22][23][24]. Since it is difficult to excite the band in the x and y directions, at the points on the lower loop (i.e..…”

Section: Comparison Of Results With Those From the Experiments And Femmentioning

confidence: 99%

A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables

Zhu¹,

Ren²,

Xiao

2011

Journal of Applied Mechanics

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A nonlinear, planar model of a slack cable with bending stiffness and arbitrarily moving ends is developed. The model uses the slope angle of the centroid line of the cable to describe the moticm of the cable, and the resulting integropartial differential equation with constraints is derived using Hamilton's principle. A new method is devehped to obtain the spatially discretized equations, and the Baumgarte stabilization procedure is used to .wive the resulting differential-algebraic equations. The model can be used to calculate the equilibria and corresponding free vibration characteristics of the cable, as well as the dynamic response of the cable under arbitrarily moving ends. The results for an equilibrium and free vibration characteristics around the equilibrium are experimentally validated on a laboratory steel band. The methodology is applied to elevator traveling and compensation cables. It is found that a vertical motion of the car can introduce a horizontal vibration of a traveling or compensation cable. The results presented are verifled by a commercial finite element software. The current method is shown to be more efficient than the finite element method as it uses a much smaller number of elements to reach the same accuracy. Some other interesting features include the condition for a traveling or compensation cable equilibrium to be closest to a natural loop and a direct proof that the catenary solution is unique.

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Section: Comparison Of Results With Those From the Experiments And Femmentioning

confidence: 99%

A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables

Zhu¹,

Ren²,

Xiao

2011

Journal of Applied Mechanics

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“…This is unimportant for a rigid body moving in time, but two points on a bent static elastic rod marked by different values of arclength cannot physically occupy the same location in space. In particular, the formulation presented here builds on the formulation in [51]. …”

Section: Variational Calculus: Necessary Conditions For Optimalitymentioning

confidence: 99%

Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review

Chirikjian¹

2015

Advanced Robotics

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Hyper-redundant (or snakelike) manipulators have many more degrees of freedom than are required to position and orient an object in space. They have been employed in a variety of applications ranging from search-and-rescue to minimally invasive surgical procedures, and recently they even have been proposed as solutions to problems in maintaining civil infrastructure and the repair of satellites. The kinematic and dynamic properties of snakelike robots are captured naturally using a continuum backbone curve equipped with a naturally evolving set of reference frames, stiffness properties, and mass density. When the snakelike robot has a continuum architecture, the backbone curve corresponds with the physical device itself. Interestingly, these same modeling ideas can be used to describe conformational shapes of DNA molecules and filamentous protein structures in solution and in cells. This paper reviews several classes of snakelike robots: (1) hyper-redundant manipulators guided by backbone curves; (2) flexible steerable needles; and (3) concentric tube continuum robots. It is then shown how the same mathematical modeling methods used in these robotics contexts can be used to model molecules such as DNA. All of these problems are treated in the context of a common mathematical framework based on the differential geometry of curves, continuum mechanics, and variational calculus. Both coordinate-dependent Euler-Lagrange formulations and coordinate-free Euler-Poincaré approaches are reviewed.

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“…Further methods that use different approaches but lead to equal results are summarized in [11]. The possibility to model a section with variable backbone curvature is examined by [12] and [13]. Both authors propose an energy based modeling technique to derive the specific kinematics of a section.…”

Section: Introductionmentioning

confidence: 99%

A variable curvature modeling approach for kinematic control of continuum manipulators

Mahl

Mayer

Hildebrandt

et al. 2013

2013 American Control Conference

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Continuum manipulators are continuously bending robots consisting of an infinite number of kinematic degrees of freedom (DOF). To reduce the number of actuators, the manipulators are designed in a way to build several serially connected groups of mechanically coupled DOF. These groups are called sections. For real-time motion control, a kinematic model capable to describe the manipulator's deflection is necessary. A common way to model the manipulator kinematics is to describe the deformation of a single section by a curve with constant curvature. This assumption constitutes an intense constrain with respect to manipulator design or model accuracy. Thus, a new kinematic modeling approach capable to describe the kinematics of continuum manipulators with variable section curvature is proposed in the present work. It subdivides a single section in a finite number of virtual units with piecewise constant curvature. This provides the possibility to shape the modeled section curvature closely to the deformation of any arbitrarily bending continuum manipulator. To demonstrate that this modeling approach is well suited for real-time control applications, simulation results of a Jacobian based feedforward pose control are presented that are applied to the common class of three actuator continuum manipulators.

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Conformational analysis of stiff chiral polymers with end-constraints

Cited by 36 publications

References 61 publications

A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables

A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables

Conformational Modeling of Continuum Structures in Robotics and Structural Biology: A Review

A variable curvature modeling approach for kinematic control of continuum manipulators

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