ABSTRACT
This paper presents the motion modeling of a cable-driven, single backbone continuum robot via the vector form intrinsic finite element (VFIFE) method. The VFIFE method is a solution framework based on vector mechanics. The algorithm describes a continuous body by using a finite number of particles instead of a mathematical function. We first approached the model by defining path elements and allocating particles (mass nodes) for the structure. We then established constitutive conditions as the generalized forces derived from both the external environment and internal deformed structural elements. We found that the dynamic equation of particles can be governed by Newton’s law of motion and solved by a general explicit time integration technique. Furthermore, we performed static modeling of the system by employing a dynamic relaxation algorithm with kinetic damping in the dynamic equations. Finally, from experiments, we validated the simulated static model of a single backbone continuum robot. It is shown that this method is capable of describing a continuum robot’s motion by solving for frame structures that undergo large deformation.
Nomenclature
/
/
displacement/velocity/acceleration vector of a particle
dt displacement of particle at current time step in time integration
displacement of particle at next time step in time integration
(,
,
) local coordinate system at t=ta
(,
,
) local coordinate system at t=t
internal force vector due to deformation in element
fN normal contact force between cable and disk
ffr induced friction force due to fN
Fext external force vector
Fg,i gravitational force at node i
Ij mass moment of inertia of particle j
,
area moment of inertia
polar moment of inertia
l, la element lengths at time t and ta
M mass matrix of a particle
rotation matrix from coordinate t=ta to t=t
Text cable pulling force
T(t) cable pulling force in time function
Ti, Ti+1 cable pulling force in vector form
u1, u2 relative change of translational nodal displacement of nodes 1 and 2
x position vector of the particle
βi relative change for nodal angle of node i
deformation of the nodal angle of node i
component of rigid body rotation angle
axial stretch of the element
component of rigid body rotation angle in
direction
rigid body rotation vector from time ta to t
ψi angle between two cable tensions of a disk
time step in time integration
coordinate transformation matrix from global to local
Acknowledgments
The financial support of Ministry of Science and Technology of Taiwan (MOST 108-2221-E-002-132-) as well as National Taiwan University (NTU) to the authors is acknowledged.
Disclosure statement
No potential conflict of interest was reported by the author(s).