0
RESEARCH PAPERS

Nonlinear Modeling of Flexible Manipulators Using Nondimensional Variables

[+] Author and Article Information
M. Chandra Shaker

 Delmia Solution Pvt. Ltd., Bangalore-560 078chandrashakeṟmulinti@delmia.com

Ashitava Ghosal1

Dept. of Mechanical Engineering, Indian Institute of Science, Bangalore 560 012, Indiaasitava@mecheng.iisc.ernet.in

The choice of coordinate systems, mode of deformation, and the boundary conditions are linked (22), and pinned boundary conditions have also been used in literature for some applications.

If M and N are same, then the number of second-order ordinary differential equations will be larger for the component-mode approach.

It may be noted that the chosen “low” and “high” actuation frequencies are much lower than the first natural frequency, which is around 380rads.

The range of the Ua values chosen, namely, from 1000to5000ms represent plastic and steel, respectively.

It may be noted that for ρA=0.1kgm, and link length of 2m, Ug=25ms represents EI=250Nm2 and Ug=45ms represents EI=810Nm2.

1

Corresponding author.

J. Comput. Nonlinear Dynam 1(2), 123-134 (Sep 11, 2005) (12 pages) doi:10.1115/1.2162866 History: Received March 03, 2005; Revised September 11, 2005

This paper deals with nonlinear modeling of planar one- and two-link, flexible manipulators with rotary joints using finite element method (FEM) based approaches. The equations of motion are derived taking into account the nonlinear strain-displacement relationship and two characteristic velocities, Ua and Ug, representing material and geometric properties (also axial and flexural stiffness) respectively, are used to nondimensionalize the equations of motion. The effect of variation of Ua and Ug on the dynamics of a planar flexible manipulator is brought out using numerical simulations. It is shown that above a certain Ug value (approximately 45ms), a linear model (using a linear strain-displacement relationship) and the nonlinear model give approximately the same tip deflection. Likewise, it was found that the effect of Ua is prominent only if Ug is small. The natural frequencies are seen to be varying in a nonlinear manner with Ua and in a linear manner with Ug.

Copyright © 2006 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Planar beam element

Grahic Jump Location
Figure 2

Modeling of a 1R kinked planar manipulator (proposed method)

Grahic Jump Location
Figure 3

Tip deflections of a 1R planar manipulator for a low frequency torque (four models): (a) 1R planar linear conventional method, (b) 1R planar linear kinked-beam method, (c) 1R planar nonlinear conventional method, and (d) 1R planar nonlinear kinked-beam method. Link length=2m(L1=1m,L2=1m), Ug=50m∕s, Ua=4800m∕s, ρA=0.1kg∕m, δ=0deg, τ1=10sin(1t)N−m.

Grahic Jump Location
Figure 4

Tip deflection of a 1R planar manipulator for a high-frequency torque (four models): Link length=2m (L1=1m, L2=1m), Ug=50m∕s, Ua=4800m∕s, ρA=0.1kg∕m, δ=0deg, τ1=10sin(10t)N−m

Grahic Jump Location
Figure 5

Tip deflection of a 1R planar manipulator with higher flexural rigidity (four models): Link length=2m (L1=1m, L2=1m), Ug=100m∕s, Ua=4800m∕s, ρA=0.1kg∕m, δ=0deg, τ1=10sin(1t)N−m

Grahic Jump Location
Figure 6

Plot of maximum tip axial and transverse deflection versus Ua: Link length=2m, ρA=0.1kg∕m, δ=0deg

Grahic Jump Location
Figure 10

(a) Plot of first natural frequency versus time and (b) Plot of first natural frequency versus Ug: Link length=2m, ρA=0.1kg∕m, τ=5sin(1t), δ=0deg, Ua=4800m∕s

Grahic Jump Location
Figure 7

Maximum tip transverse deflection for high- and low-frequency torque versus Ug: (a) τ=4sin(5t) and (b) τ=4sin(1t). Link length=2m, ρA=0.1kg∕m, δ=0deg

Grahic Jump Location
Figure 8

Plot of first and second natural frequencies versus time: Link length=2m, ρA=0.1kg∕m, τ=5sin(1t), δ=0deg, Ug=25m∕s

Grahic Jump Location
Figure 9

RMS average value of first natural frequency versus Ua: Link length=2m, ρA=0.1kg∕m, τ=5sin(1t), δ=0deg, Ug=25m∕s

Grahic Jump Location
Figure 11

Tip deflection (along the link y- and x-axes) of 1R kinked manipulator for different kink angles: Link length=2m (L1=1m, L2=1m), Ug=25m∕s, Ua=4800m∕s, ρA=0.1kg∕m, τ1=5sin(10t)N−m

Grahic Jump Location
Figure 12

Comparison between linear and nonlinear kinked manipulator with 0deg kink angle: Link length=2m, Ug=25m∕s, Ua=4800m∕s, ρA=0.1kg∕m, δ=0deg, τ1=5sin(10t)N−m

Grahic Jump Location
Figure 13

Plot of θ1 and θ2 versus nondimensional time for component- and system-mode methods: Link1=1m, Link2=1m, Ug1=100m∕s, Ua1=4800m∕s, Ug2=100m∕s, Ua2=4800m∕s, ρ1A1=0.1kg∕m, ρ2A2=0.1kg∕m, τ1=2sin(3t)N−m, τ2=0sin(0t)N−m

Grahic Jump Location
Figure 14

Plot of θ1 and θ2 versus nondimensional time for component- and system-mode methods: Link1=1m, Link2=1m, Ug1=40m∕s, Ua1=4800m∕s, Ug2=40m∕s, Ua2=4800m∕s, ρ1A1=0.1kg∕m, ρ2A2=0.1kg∕m, τ1=2sin(3t)N−m, τ2=0sin(0t)N−m

Grahic Jump Location
Figure 15

Comparison of FEM-based component- and system-mode methods of modeling 2R planar manipulator: Link1=1m, Link2=1m, Ug1=100m∕s, Ua1=4800m∕s, Ug2=100m∕s, Ua2=4800m∕s, ρ1A1=0.1kg∕m, ρ2A2=0.1kg∕m, τ1=2sin(3t)N−m, τ2=0sin(0t)N−m

Grahic Jump Location
Figure 16

Comparison of FEM-based component-and system-mode methods of modeling 2R planar manipulator: Link1=1m, link2=1m, Ug1=40m∕s, Ua1=4800m∕s, Ug2=40m∕s, Ua2=4800m∕s, ρ1A1=0.1kg∕m, ρ2A2=0.1kg∕m, τ1=2sin(3t)N−m, τ2=0sin(0t)N−m

Grahic Jump Location
Figure 17

Single-link planar manipulator (proposed approach)

Grahic Jump Location
Figure 18

Single-link planar manipulator (conventional approach)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In