RESEARCH ARTICLE

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

  • Guoxin LI 1 ,
  • Jingjun YU 1 ,
  • Yichao TANG 2 ,
  • Jie PAN 1 ,
  • Shengge CAO 1 ,
  • Xu PEI , 1
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  • 1. School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China
  • 2. Beijing Special Engineering Design and Research Institute, Beijing 100143, China
goingxu@163.com

Received date: 10 May 2022

Accepted date: 07 Sep 2022

Copyright

2023 Higher Education Press

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).

Cite this article

Guoxin LI , Jingjun YU , Yichao TANG , Jie PAN , Shengge CAO , Xu PEI . Design and modeling of continuum robot based on virtual-center of motion mechanism[J]. Frontiers of Mechanical Engineering, 2023 , 18(2) : 23 . DOI: 10.1007/s11465-022-0739-6

Nomenclature

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
Variables
a1, a2 X-coordinate of the end points B and C of link BC
b Width of the leaf
CC¯, DD ¯ Displacements of points C and D, respectively
E Elastic modulus
I, Ii Moments of inertia of the leaf and LITFP i, respectively
F Force
FCx, FCy Component forces at point C on the X- and Y-axis, respectively
FDx, FDy Component forces at point D on the X- and Y-axis, respectively
F NC, FND Axial forces applied to link DC on points C and D, respectively
FRC, FRD Radial forces exerted by link BC and AD on points C and D of link DC, respectively
hf Height of the lower plane of LITFP from the ICR
hfi 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
Hi Height of the upper plane of LITFP i from the ICR, i = 1, 2
K Bending stiffness of LITFP
KBC, KAD Bending stiffness of links BC and AD, respectively
Kd Bending stiffness of the D-LITFP
Ki Bending stiffness of the LITFP i, i = 1, 2
KV Bending stiffness of the VCM mechanism
l j oi nt( i) Driving cable length in single joint
lr Length of the rigid links A D and BC
l s eg me nt( i) Driving cable length in a single segment
l s in gl e(i) Driving cable length in half joint
l t ot al( i) Driving cable length of the whole continuum robot
M A pure bending moment
Mmax Maximum bending moment which LITFP can bear
n Position coefficient of ICR
ni 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 b en d Bending radius of the segment
RY Rotation matrix around the Y-axis
RZ Rotation matrix around the Z-axis
04R, 04P Rotation matrix and displacement vector from { O4} to { O0}, respectively
Sy Tensile yield strength
t Thickness of the leaf
ti Thickness of the leaf of LITFP i
T s eg me nt Pose transformation matrix of the single segment
T t ot al End pose transformation matrix of the whole continuum robot
01T Coordinate transformation matrix from { O1} to { O0}
02T Coordinate transformation matrix from { O2} to { O0}
12T Coordinate transformation matrix from { O2} to { O1}
α1, α2 Bending angles of link BC and AD under the action of bending moment M
σ1max, σ2max Maximum stress values corresponding to rotation angles of LITFPs 1 and 2, respectively
σdmax, σmax Maximum stress of the D-LITFP and LITFP, respectively
φ Bending angle of the half joint
φi Half of the angle between the two leaves of the LITFP i, i = 1, 2
φX, φY X- and Y-axis tilt angles, respectively
θ Rotation angle (stroke) of the VCM mechanism
θd Rotation angle of the whole D-LITFP
θdmax Maximum bending angle of the whole D-LITFP
θi, θimax (Maximum) Bending angle of the LITFP i, i = 1, 2
θjoint, θsegment Bending angles of the single joint and single segment, respectively
θmax Maximum bending angle of the LITFP
η Bending direction
ηjoint, ηsegment 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
Δ ljoint( i) Difference in driving cable length in a single joint
Δ lsegment( i) Difference in driving cable length in a single segment
Δ lsingle(i) Difference in driving cable length in half joint
Δ ltotal( i) Difference in driving cable length of the whole continuum robot

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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