A three flexure cross-hinge is an elastic joint which has a single rotational degree of freedom and consists of three seperate leafsprings.

This example shows a static simulation of a three flexure cross hinge rotating from -30 degrees (initial rotation of -30 degrees) to +30 degrees rotation (additional rotation of +60 degrees). Each leafspring is simulated with 4 beam elements rigidly connected to each other (links connecting each leafspring not shown in visualization). The dat-file is provided at the bottom of this section.

Rotational motion is pre-described by adding three stacked hinge elements with orthogonal rotation axes (equivalent to a spherical joint) and pre-describing rotational motion around the z-axis (rotation in the degree of freedom of the flexure joint) with the INPUTE argument.

HINGE 17 12 36 1 0 0
HINGE 18 36 37 0 1 0
HINGE 19 37 38 0 0 1
FIX 38 
RLSE 17 1 
RLSE 18 1 
INPUTE 19 1  

The deformation of the pre-described hinge-element is specified in the second part of the dat-file which is positioned between the arguments:

end
halt
....
INPUTE 19 1 -0.523599 
DELINPE 19 1 1.047198 
ITERSTEP 25 50 0.0000005 1 3 50
....
end
end

In this part, the INPUTE argument provides the initial rotational deformation (in radians) of the hinge element. The aditional input on top of the initial deformation is given by the DELINPE argument (in radians). When additional and initial deformations/displacements are used, the argument ITERSTEP is required. This argument controls (among other things) the number of load-steps used to solve the solution for the initial and additional load. For this example, 50 loadsteps are used for solving the initial and additional load.

ITERSTEP 25 50 0.0000005 1 3 50

Furthermore, a mass and inertia is added to the rotation center of the cross-hinge to effectively simulate an end-effector attached to the cross-hinge.

XM 11 1.000000 
XM 12	0.001000 0.000000 0.000000 0.001000 0.000000 0.001000 

First parasitic vibration mode (translational mode) at 44 Hz: Second parasitic vibration mode (translational mode) at 45 Hz: Thirth parasitic vibration mode (torsional mode) at 53Hz: Fourth parasitic vibration mode (out-of-plane bending mode)at 57Hz: Fifth parasitic vibration mode at (torsional mode) 90Hz: Sixth parasitic vibration mode at (internal mode) 243Hz:

Note: this dat-file is created with a custom matlab script and releases in the beam-elements are programmatically choosen. Therefore, the selected released deformation modes in the leaf-springs migth be non-trival.

% INNER LEAFSPRING 
X 1 -0.078218 0.063089 0.000000
X 3 -0.039109 0.031545 0.000000
X 5 0.000000 0.000000 0.000000
X 7 0.039109 -0.031545 0.000000
X 9 0.078218 -0.063089 0.000000
BEAM 1 1 2 3 4 
RLSE 1 3 5 
DYNE 1 1 2 4 6 
BEAM 2 3 4 5 6 
DYNE 2 
BEAM 3 5 6 7 8 
RLSE 3 1 
DYNE 3 2 3 4 5 6 
BEAM 4 7 8 9 10 
RLSE 4 4 6 
DYNE 4 1 2 3 5 
FIX 1 
FIX 2 

% rigid body to connect leafsprings
X 11 0.000000 0.000001 0.000000
BEAM 5	9 10 11 12 
X 13 0.008331 -0.100144 0.000000
BEAM 6	13 14 11 12 


% OUTER LEAFSPRING
X 15 0.066718 0.075146 -0.023546
X 17 0.033359 0.037573 -0.023546
X 19 0.000000 0.000000 -0.023546
X 21 -0.033359 -0.037573 -0.023546
X 23 -0.066718 -0.075146 -0.023546
BEAM 7 15 16 17 18 
RLSE 7 3 5 
DYNE 7 1 2 4 6 
BEAM 8 17 18 19 20 
RLSE 8 2 
DYNE 8 1 3 4 5 6 
BEAM 9 19 20 21 22 
DYNE 9 
BEAM 10 21 22 23 24 
RLSE 10 4 6 
DYNE 10 1 2 3 5 
FIX 15 
FIX 16 


% rigid body to connect leafsprings 
BEAM 11	23 24 11 12 


% OUTER LEAFSPRING
X 25 0.066718 0.075146 0.023546
X 27 0.033359 0.037573 0.023546
X 29 0.000000 0.000000 0.023546
X 31 -0.033359 -0.037573 0.023546
X 33 -0.066718 -0.075146 0.023546
BEAM 12 25 26 27 28 
RLSE 12 2 5 
DYNE 12 1 3 4 6 
BEAM 13 27 28 29 30 
DYNE 13 
BEAM 14 29 30 31 32 
DYNE 14 
BEAM 15 31 32 33 34 
RLSE 15 4 
DYNE 15 1 2 3 5 6 
FIX 25 
FIX 26 


% rigid body to connect leafsprings
BEAM 16	33 34 11 12 

% Hinges to actuate joint 
HINGE 17 12 36 1 0 0
HINGE 18 36 37 0 1 0
HINGE 19 37 38 0 0 1
FIX 38 
RLSE 17 1 
RLSE 18 1 
INPUTE 19 1 

% END-effector visualization
X 39 -0.066718000000000 -0.075146000000000 0
RBEAM 20 9 10 39

end 
halt 

ESTIFF 1 6210306.302256 0.667169 0.410972 569.952912 0.000283 0.000283 
EM 1 0.2321471642 0.0000213207 0.0000000154 0.0000213054 0 
ESTIFF 2 6210306.302256 0.667169 0.410972 569.952912 0.000283 0.000283 
EM 2 0.2321471642 0.0000213207 0.0000000154 0.0000213054 0 
ESTIFF 3 6210306.302256 0.667169 0.410972 569.952912 0.000283 0.000283 
EM 3 0.2321471642 0.0000213207 0.0000000154 0.0000213054 0 
ESTIFF 4 6210306.302256 0.667169 0.410972 569.952912 0.000283 0.000283 
EM 4 0.2321471642 0.0000213207 0.0000000154 0.0000213054 0 
ESTIFF 7 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 7 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 
ESTIFF 8 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 8 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 
ESTIFF 9 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 9 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 
ESTIFF 10 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 10 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 
ESTIFF 12 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 12 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 
ESTIFF 13 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 13 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 
ESTIFF 14 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 14 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 
ESTIFF 15 2415385.254432 0.240182 0.159840 33.531976 0.000043 0.000043 
EM 15 0.0902894012 0.0000012594 0.0000000060 0.0000012535 0 


XM 11 1.000000 
XM 12	0.001000 0.000000 0.000000 0.001000 0.000000 0.001000 
INPUTE 19 1 -0.523599 
DELINPE 19 1 1.047198 
ITERSTEP 25 50 0.0000005 1 3 50

end 
end 



VISUALIZATION 

BEAMPROPS 1 2 3 4 
CROSSDIM 0.033186 0.000891
DONOTDRAW 5 
DONOTDRAW 6 
BEAMPROPS 7 8 9 10 
CROSSDIM 0.012907 0.000891
DONOTDRAW 11 
BEAMPROPS 12 13 14 15 
CROSSDIM 0.012907 0.000891
DONOTDRAW 16
BEAMPROPS 20
CROSSDIM 0.01 0.06