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Design and modeling of continuum robot based on virtual-center of motion mechanism

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Abstract

Continuum robot has attracted extensive attention since its emergence. It has multi-degree of freedom and high compliance, which give it significant advantages when traveling and operating in narrow spaces. The flexural virtual-center of motion (VCM) mechanism can be machined integrally, and this way eliminates the assembly between joints. Thus, it is well suited for use as a continuum robot joint. Therefore, a design method for continuum robots based on the VCM mechanism is proposed in this study. First, a novel VCM mechanism is formed using a double leaf-type isosceles-trapezoidal flexural pivot (D-LITFP), which is composed of a series of superimposed LITFPs, to enlarge its stroke. Then, the pseudo-rigid body (PRB) model of the leaf is extended to the VCM mechanism, and the stiffness and stroke of the D-LITFP are modeled. Second, the VCM mechanism is combined to form a flexural joint suitable for the continuum robot. Finally, experiments and simulations are used to validate the accuracy and validity of the PRB model by analyzing the performance (stiffness and stroke) of the VCM mechanism. Furthermore, the motion performance of the designed continuum robot is evaluated. Results show that the maximum stroke of the VCM mechanism is approximately 14.2°, the axial compressive strength is approximately 1915 N/mm, and the repeatable positioning accuracies of the continuum robot is approximately ±1.47° (bending angle) and ±2.46° (bending direction).

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Abbreviations

Al:

alloy Aluminum alloy

CLITFP:

Compressed leaf-type isosceles-trapezoidal flexural pivot

D-LITFP:

Double leaf-type isosceles-trapezoidal flexural pivot

FEA:

Finite element analysis

ICR:

Instantaneous center of rotation

IE:

Intermediate element

LITFP:

Leaf-type isosceles-trapezoidal flexural pivot

ME:

Movement element

PLA:

Polylactic acid

PRB:

Pseudo-rigid body

S:

Stand

TLITFP:

Tensioned leaf-type isosceles-trapezoidal flexural pivot

VCM:

Virtual-center of motion

a 1, a 2 :

X-coordinate of the end points B and C of link BC

b :

Width of the leaf

\(\overline {C{C^\prime}} ,\,\,\overline {D{D^\prime}}\) :

Displacements of points C and D, respectively

E :

Elastic modulus

I, I i :

Moments of inertia of the leaf and LITFP i, respectively

F :

Force

F Cx, F Cy :

Component forces at point C on the X- and Y-axis, respectively

F Dx, F Dy :

Component forces at point D on the X- and Y-axis, respectively

F NC, F ND :

Axial forces applied to link DC on points C and D, respectively

F RC, F RD :

Radial forces exerted by link BC and AD on points C and D of link DC, respectively

h f :

Height of the lower plane of LITFP from the ICR

h fi :

Height of the lower plane of LITFP i from the ICR, i = 1, 2

H :

Height of the upper plane of LITFP from the ICR

H i :

Height of the upper plane of LITFP i from the ICR, i = 1, 2

K :

Bending stiffness of LITFP

K BC, K AD :

Bending stiffness of links BC and AD, respectively

K d :

Bending stiffness of the D-LITFP

K i :

Bending stiffness of the LITFP i, i = 1, 2

K V :

Bending stiffness of the VCM mechanism

l joint (i):

Driving cable length in single joint

l r :

Length of the rigid links A′D and B′C

l segment (i):

Driving cable length in a single segment

l single (i):

Driving cable length in half joint

l total (i):

Driving cable length of the whole continuum robot

M :

A pure bending moment

M max :

Maximum bending moment which LITFP can bear

n :

Position coefficient of ICR

n i :

Position coefficient of the ICR of the LITFP i

r :

Radius of the circle where the driving cable is located

r f :

Result of FEA

r p :

Calculation result of the PRB model

R :

Bending radius

R bend :

Bending radius of the segment

R Y :

Rotation matrix around the Y-axis

R Z :

Rotation matrix around the Z-axis

40 R, 40 P :

Rotation matrix and displacement vector from {O4} to {O0}, respectively

S y :

Tensile yield strength

t :

Thickness of the leaf

t i :

Thickness of the leaf of LITFP i

T segment :

Pose transformation matrix of the single segment

T total :

End pose transformation matrix of the whole continuum robot

10 T :

Coordinate transformation matrix from {O1} to {O0}

20 T :

Coordinate transformation matrix from {O2} to {O0}

21 T :

Coordinate transformation matrix from {O2} to {O1}

α 1, α 2 :

Bending angles of link BC and AD under the action of bending moment M

σ 1max, σ 2max :

Maximum stress values corresponding to rotation angles of LITFPs 1 and 2, respectively

σ dmax, σ max :

Maximum stress of the D-LITFP and LITFP, respectively

σ :

Bending angle of the half joint

σ i :

Half of the angle between the two leaves of the LITFP i, i = 1, 2

φ X, φ Y :

X- and Y-axis tilt angles, respectively

θ :

Rotation angle (stroke) of the VCM mechanism

θ d :

Rotation angle of the whole D-LITFP

θ dmax :

Maximum bending angle of the whole D-LITFP

θ i, θ imax :

(Maximum) Bending angle of the LITFP i, i = 1, 2

θ joint, θ segment :

Bending angles of the single joint and single segment, respectively

θ max :

Maximum bending angle of the LITFP

η :

Bending direction

η joint, η segment :

Bending directions of the single joint and single segment, respectively

ε :

Relative error of PRB model with respect to FEA

Δl :

Displacement of the force sensor

Δl(i):

Cable length difference

Δl joint(i):

Difference in driving cable length in a single joint

Δl segment(i):

Difference in driving cable length in a single segment

Δl single(i):

Difference in driving cable length in half joint

Δl total(i):

Difference in driving cable length of the whole continuum robot

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. U1813221) and the National Key R&D Program of China (Grant No. 2019YFB1311200).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Beihang University, Beijing, 100191, China

    Guoxin Li, Jingjun Yu, Jie Pan, Shengge Cao & Xu Pei

  2. Beijing Special Engineering Design and Research Institute, Beijing, 100143, China

    Yichao Tang

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  1. Guoxin Li
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Correspondence to Xu Pei.

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Li, G., Yu, J., Tang, Y. et al. Design and modeling of continuum robot based on virtual-center of motion mechanism. Front. Mech. Eng. 18, 23 (2023). https://doi.org/10.1007/s11465-022-0739-6

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