Screw Theoretic View on Dynamics of Spatially Compliant Beam

DING Xi-lun; DING Xi-lun

doi:10.3879/j.issn.1000-0887.2010.09.011

Volume 31 Issue 9

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DING Xi-lun, DING Xi-lun. Screw Theoretic View on Dynamics of Spatially Compliant Beam[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011

Citation:

DING Xi-lun, DING Xi-lun. Screw Theoretic View on Dynamics of Spatially Compliant Beam[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011

Citation:

DING Xi-lun, DING Xi-lun. Screw Theoretic View on Dynamics of Spatially Compliant Beam[J]. Applied Mathematics and Mechanics, 2010, 31(9): 1118-1132. doi: 10.3879/j.issn.1000-0887.2010.09.011

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Screw Theoretic View on Dynamics of Spatially Compliant Beam

doi: 10.3879/j.issn.1000-0887.2010.09.011

DING Xi-lun¹,
DING Xi-lun²

1.
Robotics Research Institute, Beihang University, Beijing 100191, P. R. China;

Received Date: 1900-01-01
Rev Recd Date: 2010-08-12
Publish Date: 2010-09-15

Abstract

Abstract

Beam with spatial compliance can be deformed as bending in the plane,twisting and extending. In terms of the screw theory on rigid body motion,the concept of‘deflection screw' was introduced,spatial compliant beam theory via the deflection screw was then proposed,and the spatial compliance of such a beam system was presented and analysed based on material theory and fundamental kinematic assumptions. To study the dynamics of spatially compliant beam,the potential energy and the kinetic energy of the beam were discussed using screw theory,and then,the lagrangian was obtained.The Rayleigh-Ritz method was further used to compute the vibrational frequencies after a discussion of boundary conditions and shape functions.The eigenfrequencies of the beam with spatial compliance were compared with that of individual deformation cases,pure bending,extension or torsion.Finally,dynamics of a robot with two spatial compliant links and perpendicular joints was studied using the spatial compliant beam theory,and the coupling effects between the joint rigid body motions and the deformations of spatial compliant links can be easily found by our dynamic simulation.The study convinces that the effectiveness of using screw theory to deal with the problems of dynamic modeling and analysis of mechanisms with spatially compliant links.
- spatial compliance,
- beam,
- deformation,
- dynamics

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References(14)

References

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