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Research Papers

# Modeling of a Cartwheel Flexural Pivot

[+] Author and Article Information
Bi Shusheng

Robotics Institute, Beihang University, Beijing, 100191, P.R.C.biss_buaa@163.com

Zhao Hongzhe

Robotics Institute, Beihang University, Beijing, 100191, P.R.C.hongzhezhao@gmail.com

Yu Jingjun

Robotics Institute, Beihang University, Beijing, 100191, P.R.C.jjyu@buaa.edu.cn

1

Corresponding author.

J. Mech. Des 131(6), 061010 (May 21, 2009) (9 pages) doi:10.1115/1.3125204 History: Received July 10, 2008; Revised March 16, 2009; Published May 21, 2009

## Abstract

A cartwheel flexural pivot has a small center shift as a function of loading and ease of manufacturing. This paper addresses an accurate model that includes the loading cases of a bending moment combined with both a horizontal force and a vertical force. First, a triangle flexural pivot is modeled as a single beam. Then, the model of cartwheel flexural pivot based on an equivalent model is developed by utilizing the results of the triangle pivot. The expressions for rotational displacement and center shift are derived to evaluate the primary motion and the parasitic motion; the maximum rotational angle is simply formulated to predicate the range of motion. Finally, the model is verified by finite element analysis. The relative error of the primary motion is less than 1.1% for various loading cases even if the rotational angle reaches ±20 deg, and the predicted errors for the two center shift components are less than 15.4% and 7.1%. The result shows that the model is accurate enough for designers to use for initial parametric design studies, such as for conceptual design.

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## Figures

Figure 1

(a) A cross-spring pivot and (b) a cartwheel flexural pivot

Figure 2

A beam flexure

Figure 3

The model of the triangle flexural pivot

Figure 4

(a) Deflected triangle flexural pivot, (b) enlarged schematic for the center shift of the triangle flexural pivot, and (c) loads and displacements in the deflected triangle flexural pivot

Figure 5

A beam under loads and the corresponding bending moment diagram

Figure 6

The equivalent model of a cartwheel flexural pivot

Figure 7

Rotational displacement for different loads f and p

Figure 8

Rotational displacement for different loads m and p

Figure 9

Rotational displacement for different loads m and f

Figure 10

X component of center shift for different loads f and p

Figure 18

Both components of center shift for different angle α

Figure 17

Rotational displacement for different angle α

Figure 16

Improved X component of center shift for different loads f and p

Figure 11

Y component of center shift for different loads f and p

Figure 15

Y component of center shift for different loads m and f

Figure 14

X component of center shift for different loads m and f

Figure 13

Y component of center shift for different loads m and p

Figure 12

X component of center shift for different loads m and p

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