Is the Kinematics of 3D Space Truss Affected by Closed Loops in the System?

In summary, the conversation is about a PhD student's research on analyzing the rigidity of a structure of rigid beams in 3D. The student presents a diagram of the structure and discusses the possibility of it being able to move. They also ask for a theory to help understand the problem. The conversation then delves into terminology and notations, specifically regarding joints and degrees of freedom. The student provides examples of different types of triangles and their degrees of freedom, and the conversation concludes with a discussion on the constraints and dofs of the structure. The student is still unsure about the number of rotations a thin truss should have.
  • #36
chingkui said:
didn't try to go through all posts here, but are you looking for the Chebychev–Grübler–Kutzbach's criterion in 3D?

I must admit to have never heard about this criterion before, but from the definition on wikipedia it seems that the answer to this question is yes. So do you think it is possible to apply it to my case? Would it work with the hexagon trivial example?

From more googling, it seems that the criterion fails when there are closed loops in the system. This might be bypassed using the "dual" representation of my rigid triangles connected by ball joints (shown in post #27), that is by observing that triangles can bend only about the hinges.
 
<h2> How do closed loops affect the kinematics of 3D space truss? </h2><p>Closed loops in a 3D space truss can affect the kinematics of the system by introducing additional forces and moments, which can alter the overall structural behavior. This can lead to changes in the displacement, velocity, and acceleration of the truss elements.</p><h2> Can closed loops in a 3D space truss cause instability? </h2><p>Yes, closed loops in a 3D space truss can cause instability if they are not properly accounted for in the design and analysis. The additional forces and moments introduced by the closed loops can lead to unexpected deformations and failure of the truss structure.</p><h2> How can closed loops be incorporated into the kinematic analysis of a 3D space truss? </h2><p>Closed loops can be incorporated into the kinematic analysis of a 3D space truss by using methods such as the finite element method or matrix structural analysis. These methods allow for the inclusion of closed loops in the overall structural model and can accurately predict their effects on the kinematics of the truss.</p><h2> Are there any benefits to including closed loops in a 3D space truss design? </h2><p>Yes, closed loops can provide additional support and stability to the truss structure. They can also allow for more efficient use of materials and can help distribute forces more evenly throughout the truss.</p><h2> How do closed loops in a 3D space truss affect the overall strength of the structure? </h2><p>The presence of closed loops in a 3D space truss can increase the overall strength of the structure, as they can help distribute forces and resist deformation. However, if not properly accounted for, closed loops can also introduce weak points in the truss and decrease its overall strength.</p>

FAQ: Is the Kinematics of 3D Space Truss Affected by Closed Loops in the System?

How do closed loops affect the kinematics of 3D space truss?

Closed loops in a 3D space truss can affect the kinematics of the system by introducing additional forces and moments, which can alter the overall structural behavior. This can lead to changes in the displacement, velocity, and acceleration of the truss elements.

Can closed loops in a 3D space truss cause instability?

Yes, closed loops in a 3D space truss can cause instability if they are not properly accounted for in the design and analysis. The additional forces and moments introduced by the closed loops can lead to unexpected deformations and failure of the truss structure.

How can closed loops be incorporated into the kinematic analysis of a 3D space truss?

Closed loops can be incorporated into the kinematic analysis of a 3D space truss by using methods such as the finite element method or matrix structural analysis. These methods allow for the inclusion of closed loops in the overall structural model and can accurately predict their effects on the kinematics of the truss.

Are there any benefits to including closed loops in a 3D space truss design?

Yes, closed loops can provide additional support and stability to the truss structure. They can also allow for more efficient use of materials and can help distribute forces more evenly throughout the truss.

How do closed loops in a 3D space truss affect the overall strength of the structure?

The presence of closed loops in a 3D space truss can increase the overall strength of the structure, as they can help distribute forces and resist deformation. However, if not properly accounted for, closed loops can also introduce weak points in the truss and decrease its overall strength.

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