# Tie-System Calibration for the Experimental Setup of Large Deployable Reflectors

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

- Photogrammetry,
- Laser tracker, and
- Laser radar.

## 2. Experimental Settings for Calibration

#### 2.1. Rigid Ring Truss Support: Construction Length Determination

`fsolve`, but it does not allow the inclusion of any constraints. To overcome this problem, the nonlinear programming solver

`fmincon`can be used by giving a constant objective function and setting (1) as the nonlinear equality constraint, in addition to the linear inequality constraint ${L}_{ij}\ge {L}_{ij}^{0}$. The resulting constrained optimization problem is described below:

#### 2.2. Rear Node Determination

#### 2.3. Rigid Ring Truss Support: Tie Calibration

#### 2.4. Flexible Ring Truss Support

## 3. Results

- Focal length: 6 m
- Number of free nodes: 296
- Number of vertices: 14
- Number of total cables: 1044
- Cable section: 4 mm
^{2} - Young modulus of cables: $8.3\times {10}^{10}$ N/m
^{2} - Initial RMS error: 0.5872 mm
- Design value of the RMS faceting error: 0.21 mm

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MDPI | Multidisciplinary Digital Publishing Institute |

DOAJ | Directory of open access journals |

TLA | Three letter acronym |

LD | linear dichroism |

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**Figure 4.**Layout of a cable: The construction length ${L}_{0}$ is affected by manufacturing errors generated during the cutting operation and assembly errors coming from a bad placement of the eyelets necessary to connect two or more cables.

**Figure 5.**Screw adjustment in the tie system: (

**left**) Tie system before adjustment; and (

**right**) tie system after the screw regulation.

**Figure 8.**Pie chart of the error (absolute value), grouped by measuring ranges (mm), between the measured construction lengths and those obtained by solving for equilibrium in System (1).

**Figure 11.**Faceting error (mm) distribution on the front tension truss, obtained for the rigid ring truss support.

**Figure 13.**Faceting error (mm) distribution on the front tension truss, obtained for the flexible ring truss support.

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## Share and Cite

**MDPI and ACS Style**

Cammarata, A.; Sinatra, R.; Rigato, R.; Maddio, P.D.
Tie-System Calibration for the Experimental Setup of Large Deployable Reflectors. *Machines* **2019**, *7*, 23.
https://doi.org/10.3390/machines7020023

**AMA Style**

Cammarata A, Sinatra R, Rigato R, Maddio PD.
Tie-System Calibration for the Experimental Setup of Large Deployable Reflectors. *Machines*. 2019; 7(2):23.
https://doi.org/10.3390/machines7020023

**Chicago/Turabian Style**

Cammarata, Alessandro, Rosario Sinatra, Riccardo Rigato, and Pietro Davide Maddio.
2019. "Tie-System Calibration for the Experimental Setup of Large Deployable Reflectors" *Machines* 7, no. 2: 23.
https://doi.org/10.3390/machines7020023