# A Reconfigurable Parallel Robot for On-Structure Machining of Large Structures

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## Abstract

**:**

## 1. Introduction

- Using reconfiguration by reassembly, we have a lighter robot when the basic build of the robot with three actuators is used. With other on-structure parallel robots having five or more actuators, the larger number of actuators results in larger weight. This is because such robots with five or more actuators have fixed topology, and hence, all their actuators should always be mounted on the robots although the robots are performing three-axis machining tasks.
- The modular design of the robot results in easier and less costly maintenance. When any additional module needs replacement, one can replace only that particular module, without a need to replace the whole robot. Replacement of such components is also easier due to the modular design.
- The modular robot can be sold as multiple packages using the same basic build. Each robot package is sold with its own topology and number of DOFs. The use of the same basic build for the various packages gives an advantage to the manufacturer in terms of the design, production, and sales. This is due to the modularity of the robot. On the user side, the purchase of the modular robot can be performed in multiple phases. One may start procuring the three-axis basic build with lower cost. This three-axis robot can already be used for three-axis machining tasks. At a later time, the additional modules can be procured when they are required.
- The joint motion planning in the three-axis motion, in both the reassembly and joint locking schemes, is simpler as the robot uses only three actuators. In contrast, other on-structure parallel robots with five or more actuators need to involve all of their actuators in the joint motion planning even when they are used for three-axis motion.

## 2. Topology

## 3. Mobility Analysis

#### 3.1. Mobility of 3SPR Mechanism

#### 3.2. Mobility of 3SU Mechanism

## 4. Pose Kinematics

#### 4.1. Pose Kinematics of 3PRPR, 3PRRR, and Serial RR Mechanisms

_{1}, x

_{2}, and x

_{3}) and end-effector position (x,y,z). In an actual implementation, there may be constant offsets between them. Since the kinematics of this mechanism is straightforward, it is not discussed in this paper.

#### 4.2. Pose Kinematics of 3SPR Mechanism

_{1}A

_{2}A

_{3}and B

_{1}B

_{2}B

_{3}, respectively. The circumradii of both triangles are, respectively, $R$ and $r$. The positions of the points A

_{1}, A

_{2}, and A

_{3}in the XYZ frame are given by the vectors ${\mathit{a}}_{\mathit{1}}$, ${\mathit{a}}_{\mathit{2}}$, and ${\mathit{a}}_{\mathit{3}}$, respectively, whereas the positions of the points B1, B2, and B3 in the X′Y′Z′ frame are given by the following vectors ${}_{}{}^{\mathit{P}}\mathit{b}{}_{\mathit{1}}$, ${}_{}{}^{\mathit{P}}\mathit{b}{}_{\mathit{2}}$, and ${}_{}{}^{\mathit{P}}\mathit{b}{}_{\mathit{3}}$, respectively.

_{,}which represent the rotation of the moving platform about the X, Y, and Z axes. However, as discussed in the mobility analysis, the rotation about the Z axis is coupled with translation.

**P**preceding a vector indicates that the vector is expressed in the X′Y′Z′ frame. A vector not preceded by any superscript is expressed in the XYZ frame.

**b**and leg

_{i}**l**are always perpendicular to the axis of the passive revolute joint i, each limb creates a plane, namely AA

_{i}_{i}B

_{i}P. Consequently, the sum of the vectors

**p**and

**b**is also always perpendicular to the axis of the passive revolute joint ${\mathit{w}}_{\mathit{i}}$. This can be written as the following zero dot product:

_{i}#### 4.3. Pose Kinematics of the 3SU Mechanism

**p**denotes the position of the center of the moving platform P with respect to point A, whereas the matrix ${\mathit{R}}_{\mathit{A}}^{\mathit{P}}$ is a rotation matrix representing the rotation of the moving platform, i.e., the moving frame X′Y′Z′, with respect to the base, i.e., the XYZ frame. Since the R joints in each U joint rotate about the X and Y axes of a local frame which has the origin B

_{i}and the Z direction aligned with the leg direction, the rotation of both the R joints can be represented by the rotation matrices ${\mathit{R}}_{\mathit{x}}$ and ${\mathit{R}}_{\mathit{y}}$ that, respectively, represent the elementary rotation matrices about the X and Y axes. The angles denote the magnitude of the rotations ${\theta}_{ai}$ and ${\theta}_{pi}$ that, respectively, denote the angles of the active and passive R joints of the U joint in the i-th limb. The vector ${}_{}{}^{{\mathit{B}}_{\mathit{i}}}\mathit{l}{}_{\mathit{i}}$ is the i-th leg vector expressed at its local frame that has the origin B

_{i}, that is:

#### 4.4. Pose Kinematics of the Combined Mechanism

_{N}Y

_{N}Z

_{N}. In other words, the position of the whole mechanism in the world frame is given by the vector $\overrightarrow{\mathrm{NA}}$. This vector is constant when the whole mechanism is attached to the surface of the workpiece/structure, whereas the vector changes when the mechanism is walking. The X′Y′Z′ frame is attached to the moving platform of the 3SPR mechanism which serves as the base of the 3PRPR mechanism.

_{p.}

#### 4.5. Numerical Example

_{1}, L

_{2}, and L

_{3,}are expressed as constants representing the lengths of the actuated P joints. The actuator positions of both the variations in the SRꞱR (SU) mechanism, namely ${\theta}_{a1}$, ${\theta}_{a2}$, and ${\theta}_{a3}$, are expressed as constants representing the angles of the actuated R joints. The end-effector pose (x,y,z) and the end-effector orientation (${\theta}_{x}$, ${\theta}_{y}$, ${\theta}_{z}$) are expressed in the XYZ frame. Figure 14 and Figure 15, respectively, show the plots of the 3SPR-3PRPR and 3SU-3PRPR mechanisms in the XYZ frame.

## 5. Differential Kinematics and Singularity Analysis

#### 5.1. Differential Kinematics and Singularity Analysis of 3PRPR and 3PRRR Mechanisms

#### 5.2. Differential Kinematics and Singularity Analysis of 3SPR Mechanism

_{i}and B

_{i}, a unique screw that is reciprocal to all the unactuated joint screws is:

_{1}, L

_{2}, and L

_{3}, such that the moving platform cannot collapse to the base. Second, an architectural singularity occurs if the three actuation forces are parallel, as depicted in Figure 16a. This only occurs if the moving platform and the base have identical geometry and dimensions. Thus, this singularity can be easily avoided by making the moving platform smaller than the base. Third, an architectural singularity occurs if any of the P joint axes are collinear with the vector ${\mathit{b}}_{\mathit{i}}$ of the moving platform, as illustrated in Figure 16b.

#### 5.3. Differential Kinematics and Singularity Analysis of 3SU Mechanism

## 6. Workspace

#### 6.1. Workspace of the 3T Mechanism

#### 6.2. Workspace of the Serial RR Mechanism

#### 6.3. Workspace of the 3SPR and 3SU Mechanisms

## 7. Reconfiguration Schemes

## 8. Dimensional Optimization

#### 8.1. Optimization of the 3T Mechanism

#### 8.2. Optimization of the Serial RR Mechanism

#### 8.3. Optimization of the 3SPR and 3SU Mechanisms

#### 8.3.1. Design Variables

#### 8.3.2. Optimization Constraints

#### 8.3.3. Objective Function

_{x}and θ

_{y,}maximizing the range of each angle can be written as maximizing the difference between the maximum and minimum limits of each angle, i.e., ${\theta}_{x,max}-{\theta}_{x,min}$ and ${\theta}_{y,max}-{\theta}_{y,min}$

_{.}Since there are two ranges of angles to be maximized, it is more practical in the optimization algorithm to combine both as a single objective given by the sum of them. Hence, the single objective function can be written as the following weighted sum:

#### 8.3.4. Optimization Formulation

- the lower and upper bounds of $R$ as written in Equation (36);
- the lower and upper bounds of $r$ as written in Equation (36);
- the inequality constraint written in Equation (38);
- the limits of the S joints, i.e., ${\theta}_{pj,min}^{is}\le {\theta}_{pj}^{is}\le {\theta}_{pj,max}^{is}$ for i = 1,2,3 and j = 1,2,3;
- the limits of the R joints, i.e., ${\theta}_{pi,min}\le {\theta}_{pi}\le {\theta}_{pi,max}$ for i = 1,2,3;
- the interference constraints written in Equations (39) and (40).

- the lower and upper bounds of $R$ as written in Equation (36);
- the lower and upper bounds of $r$ as written in Equation (36);
- the lower and upper bounds of ${L}_{i}$ as written in Equation (37);
- the inequality constraint written in Equation (38);
- the limits of the S joints, i.e., ${\theta}_{pj,min}^{i}\le {\theta}_{pj}^{i}\le {\theta}_{pj,max}^{i}$ for i = 1,2,3 and j = 1,2,3;
- the limits of the U joints, i.e., ${\theta}_{ai,min}\le {\theta}_{ai}\le {\theta}_{ai,max}$ and ${\theta}_{pi,min}\le {\theta}_{pi}\le {\theta}_{pi,max}$ for i = 1,2,3;
- the interference constraints written in Equations (39) and (40).

#### 8.3.5. Optimization Algorithm

- Step 1: Run the forward kinematics of the mechanism by inputting the active joints’ positions at a specific discretization interval within their ranges. The tilting angles of the moving platform ${\theta}_{x}$ and ${\theta}_{y}$ corresponding to the input active joints’ positions are obtained from the forward kinematics solution. It is worth mentioning that the lower and upper limits of the active P joints, ${L}_{i,min}$ and ${L}_{i,max}$, determined a priori in the 3SPR mechanism, can be considered pre-determined constraints that are not part of the optimization. Similarly, the limits of the active joints in the 3SU mechanism that are determined a priori can also be considered pre-determined constraints that are not part of the optimization.
- Step 2: Extract the minimum and maximum values of the obtained tilting angles of the moving platform ${\theta}_{x}$ and ${\theta}_{y}$. This gives us ${\theta}_{x,min}$, ${\theta}_{x,max}$, ${\theta}_{y,min}$, and ${\theta}_{y,max}$.
- Step 3: Compute the objective function written in Equations (41) or (42), depending on whether it is maximization or minimization.

#### 8.3.6. Numerical Example

^{®}Xeon

^{®}processor and 64 GB RAM, the optimization of the 3SPR with forward kinematics discretization interval of 0.01 m took 340 min. On the other hand, the optimization of the 3SU mechanisms with the forward kinematics discretization interval of 0.01 deg took 1125 min. The optimization stopped after the average change in the fitness value is less than the function tolerance. The optimization of the 3SPR mechanism gives the following optimized design variables: R = 0.549 m and r = 0.205 m. On the other hand, the optimization of the 3SU mechanism gives the following optimized design variables: R = 0.533 m, r = 0.234 m, and ${L}_{1}={L}_{2}={L}_{3}=$ 0.493 m.

## 9. Design Considerations

## 10. Conclusions

## 11. Patent

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Appendix A

Abbreviation | Meaning |
---|---|

DOF | Degree of freedom |

P, R, U, S | Prismatic, revolute, universal, and spherical joints |

A | Attachment |

3T | Three-translation |

2R | Two-rotation |

3R | Three-rotation |

3T2R | Three-translation and two-rotation |

1T2R | One-translation and two-rotation |

TCP | Tool Center Point |

## Appendix B

Symbol | Meaning |
---|---|

Ʇ | Perpendicularity between two adjacent joint axes |

Underline | Actuated joint |

${\$}^{\mathit{i}}$ | Joint screws in the i-th limb |

${\$}_{\mathit{j}}^{\mathit{i}}$ | Screw of the j-th joint in the i-th limb |

${\$}^{\mathit{i}\mathit{r}}$ | Reciprocal screw in the i-th limb |

x_{1}, x_{2}, x_{3} | Positions of the three active P joints in the 3T mechanism |

x,y,z | End-effector position |

${\mathrm{x}}_{\mathrm{i}}{y}_{\mathrm{i}}{z}_{\mathrm{i}}$ | Coordinate frame of the i-th limb |

xyz | Coordinate frame attached to the apex of the pyramid of 3T mechanism |

XYZ | Coordinate frame attached to the center of the base of the lower mechanism |

X′Y′Z′ | Coordinate frame attached to the moving platform of the lower mechanism |

X″Y″Z″ | Coordinate frame attached to a tip of the pyramid segments of the 3T mechanism |

X_{N}Y_{N}Z_{N} | Inertial (world) coordinate frame |

$\mathit{p}$ | Position vector of the moving platform with respect to the center of the base |

${\mathit{R}}_{\mathit{A}}^{\mathit{P}}$ | Rotation matrix of the moving platform with respect to the base |

${\mathit{R}}_{\mathit{x}}$$,\text{}{\mathit{R}}_{\mathit{y}}$ | Elementary rotation matrix about X and Y axes |

${\theta}_{x,}{\theta}_{y,}{\theta}_{z}$ | Tilting angles of the moving platform with respect to X, Y, and Z axes |

${\theta}_{x,min},{\theta}_{x,max}$ | Minimum and maximum values of ${\theta}_{x}$ |

${\theta}_{y,min},{\theta}_{y,max}$ | Minimum and maximum values of ${\theta}_{y}$ |

${\theta}_{ai}$$,\text{}{\theta}_{pi}$ | Angles of the active and passive R joints of the R or U joint in the i-th limb |

${\theta}_{ai,min,}{\theta}_{ai,max}$ | Minimum and maximum values of ${\theta}_{ai}$ |

${\theta}_{pi,min,}{\theta}_{pi,max}$ | Minimum and maximum values of ${\theta}_{pi}$ |

${\theta}_{pj}^{is}$ | Angle of the i-th rotational DOF of the S joint in the j-th limb |

${\theta}_{pj,min,}^{is}{\theta}_{pj,min}^{is}$ | Minimum and maximum values of ${\theta}_{pj}^{is}$ |

R | Circumradius of the base |

${R}_{min},{R}_{max}$ | Minimum and maximum values of R |

r | Circumradius of the moving platform |

${r}_{min},{r}_{max}$ | Minimum and maximum values of r |

${}_{}{}^{A}\mathit{r}$ | Position vector r expressed with respect to point A |

${\mathit{a}}_{\mathit{i}}$ | Position vector of the i-th S joint with respect to the base center |

${\mathit{b}}_{\mathit{i}}$ | Position vector of the i-th distal joint with respect to the moving platform center |

${\mathit{d}}_{\mathit{i}}$ | Position vector of the active P joint in the 3SPR mechanism |

L_{p} | Length of each of the pyramid segments |

${L}_{i}$ | Stroke length of the i-th actuator in the 3SPR mechanism |

${L}_{i,min},{L}_{i,max}$ | Minimum and maximum values of ${L}_{i}$ |

L | Constant length of the link connecting the S and U joints in the SU mechanism |

${\mathit{l}}_{\mathit{i}}$ | Unit directional vector of the i-th active P joint in the 3SPR mechanism |

${\mathit{w}}_{\mathit{i}}$ | Unit directional vector of the R joint in the i-th U joint perpendicular to ${\mathit{b}}_{\mathit{i}}$ |

${\mathit{v}}_{\mathit{i}}$ | Unit directional vector of the R joint in the i-th U joint perpendicular to ${\mathit{w}}_{\mathit{i}}$ |

${\$}_{\mathit{P}}$ | Instantaneous twist of the moving platform |

${\omega}_{x},{\omega}_{y},{\omega}_{z}$ | Angular velocities of the moving platform with respect to X, Y, and Z axes |

$\dot{x},\dot{y},\dot{z}$ | Translational velocities of the moving platform in the X, Y, and Z directions |

$\dot{\mathit{q}}$ | Twist of the actuators |

${\dot{\theta}}_{j}^{i},{\dot{d}}_{j}$ | Intensity of the j-th rotational and translational joints in the i-th limb |

${\widehat{\$}}_{\mathit{j}}^{\mathit{i}}$ | j-th unit joint screw in the i-th limb |

${\mathit{s}}_{\mathit{j}}^{\mathit{i}}$ | s vector of the j-th unit joint screw in the i-th limb |

${\mathit{e}}_{\mathit{i}}$ | i-th actuation vector |

${\mathit{J}}_{\mathit{x}}$ | Forward Jacobian matrix |

${\mathit{J}}_{\mathit{q}}$ | Inverse Jacobian matrix |

${\mathit{J}}_{\mathit{a}}$ | Actuation Jacobian matrix |

${\mathit{J}}_{\mathit{c}}$ | Constraint Jacobian matrix |

$\mathit{J}$ | Overall Jacobian matrix |

${f}_{maximization}$ | Maximization objective function |

${f}_{minimization}$ | Minimization objective function |

${g}_{i}$ | Weight of the i-th objective in the weighted sum |

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**Figure 1.**(

**a**) Schematic and (

**b**) implementation of the 3PRPR on-structure robot with 3T manipulation capability.

**Figure 2.**(

**a**) Schematic and (

**b**) implementation of the 3PRRR on-structure robot with 3T manipulation capability.

**Figure 3.**The three-axis robot is attached to (

**a**) a flat surface and (

**b**) a section of a spherical surface.

**Figure 4.**(

**a**) The schematic and (

**b**) implementation of the 3T2R robot achieved by adding an active 2R module to the moving platform.

**Figure 5.**(

**a**) The schematic and (

**b**) implementation of the 6-DOF robot achieved by adding SPR chains, with actuated P joints, to the 3T mechanism.

**Figure 7.**The addition of SRꞱR (SU) chains to the 3T mechanism by using the first U joint configuration in which (

**a**) the intermediate R joints of the SRꞱR kinematic chains intersect at a common point in their initial posture while the last R joints are actuated and (

**b**) the axes of the last R joints of the SRꞱR kinematic chains are fixed in a perpendicular position with respect to the segments of the pyramid frame, making an equilateral triangle.

**Figure 8.**The addition of SRꞱR (SU) chains to the 3T mechanism by using the second U joint configuration in which (

**a**) the last R joints of the SRꞱR kinematic chains intersect at a common point while the intermediate R joints are actuated and (

**b**) the axes of the intermediate R joints of the SRꞱR kinematic chains make an instantaneous equilateral triangle in the initial posture.

**Figure 10.**In its initial posture, (

**a**) the i-th limb joint screws and (

**b**) constraint screws in the 3SU mechanism.

**Figure 13.**The schematic of (

**a**) the 3SPR-3PRPR (or 3SPR-3PRRR) mechanism and (

**b**) 3SU-3PRPR (or 3SU-3PRRR) mechanism.

**Figure 14.**Three-dimensional view plot of the 3SPR-3PRPR mechanism with the end-effector E in an orientation of (0, 0, 0) and position coincident with the center of the moving platform of the lower mechanism.

**Figure 15.**Three-dimensional view plot of the 3SU-3PRPR mechanism with the end-effector E in an orientation of (5, 0, 0) degrees and position coincident with the center of the pyramid base.

**Figure 16.**(

**a,b**) Two configurations having architectural singularities in the 3SPR mechanism, (

**c**) the constraint singularity configuration in the 3SPR mechanism, and (

**d**) an architectural singularity in the 3SU mechanism.

**Figure 17.**(

**a**) The workspace of the 3T mechanism, (

**b**) serial RR mechanism with two non-zero links, and (

**c**) total orientation workspace of the serial RR mechanism shown in (

**b**) given the tilting range of both the R joints between −90 and 90 degrees.

**Figure 18.**The total orientation workspaces of the 3SPR mechanism with (

**a**) R = 0.3 m, ${L}_{i},min$ = 0.2 m, ${L}_{i},max$ = 0.6 m, and (

**b**) R = 0.5 m, ${L}_{i},min$ = 0.2 m, ${L}_{i},max$ = 0.6 m, and (

**c**) the total orientation workspace of the 3SU mechanism with R = 0.5 m, r = 0.3 m. All the mechanisms use the S joints with a rotational motion range between −30 and 30 degrees.

**Figure 19.**Two possible reconfiguration scenarios using modularity: (

**a**) the attachment pad and spherical joint are included in each module, and (

**b**) the attachment pad and spherical joint are made as separate modules.

**Figure 20.**Reconfiguration by joint locking in the (

**a**) serial RR chain, (

**b**) SPR chain, (

**c**) first variant of SU chain, and (

**d**) second variant of SU chain.

**Figure 21.**(

**a**) Three-dimensional and (

**b**–

**d**) two-dimensional plots of the orientation workspace of the optimized 3SPR mechanism. The dots, regardless of their color, represent the reachable tilting angles.

**Figure 22.**The optimized 3SPR mechanism tilted at (

**a**) ${\theta}_{x}=-20deg,{\theta}_{y}={\theta}_{z}=0$, (

**b**) ${\theta}_{x}=10deg,{\theta}_{y}={\theta}_{z}=0$, (

**c**) ${\theta}_{x}=0,{\theta}_{y}=-15deg,{\theta}_{z}=0$, and (

**d**) ${\theta}_{x}=0,{\theta}_{y}=15deg,{\theta}_{z}=0$.

**Figure 23.**(

**a**–

**c**) Two-dimensional plots of the orientation workspace of the optimized 3SU mechanism with the rotational range of the S and U joints between −80 deg and 80 deg. The dots, regardless of their color, represent the reachable tilting angles.

**Figure 24.**The optimized 3SU mechanism with the rotational range of the S and U joints between −80 deg and 80 deg tilted at (

**a**) ${\theta}_{x}=-70deg,{\theta}_{y}={\theta}_{z}=0$ and (

**b**) ${\theta}_{x}=60deg,{\theta}_{y}={\theta}_{z}=0$.

**Figure 25.**(

**a**–

**c**) Two-dimensional plots of the orientation workspace of the optimized 3SU mechanism with the rotational range of the S and U joints between −30 deg and 30 deg. The dots, regardless of their color, represent the reachable tilting angles.

**Figure 26.**The optimized 3SU mechanism with the rotational range of the S and U joints between −30 deg and 30 deg tilted at (

**a**) ${\theta}_{x}=-10deg,{\theta}_{y}={\theta}_{z}=0$, (

**b**) ${\theta}_{x}=10deg,{\theta}_{y}={\theta}_{z}=0$, (

**c**) ${\theta}_{x}=0,{\theta}_{y}=-10deg,{\theta}_{z}=0$, and (

**d**) ${\theta}_{x}=0,{\theta}_{y}=10deg,{\theta}_{z}=0$.

Mechanism | Actuator Position | End-Effector Pose |
---|---|---|

3SPR-3PRPR | ${x}_{1}$$={x}_{2}$$={x}_{3}$= 0.1667 m L _{1} = L_{2} = L_{3} = 0.3262 m | x = 0, y = 0, z = 0.3000 m ${\theta}_{x}$$={\theta}_{y}$$={\theta}_{z}$= 0 |

3SRꞱR-3PRPR | ${x}_{1}$$={x}_{2}$$={x}_{3}$= 0.1667 m ${\theta}_{a1}$$=-19.2743\mathrm{deg},{\theta}_{a2}$= 0, ${\theta}_{a3}$$=19.2743\mathrm{deg}$ | x = 0, y = 0.0948 m, z = 0.2651 m ${\theta}_{x}$$=5\text{}\mathrm{deg},\text{}{\theta}_{y}$$={\theta}_{z}$= 0 |

3SRꞱR-3PRPR | ${x}_{1}$$={x}_{2}$$={x}_{3}$= 0.1667 m ${\theta}_{a1}$$=-16.7787\mathrm{deg},{\theta}_{a2}$= 0, ${\theta}_{a3}$$=16.7786\mathrm{deg}$ | x = 0, y = 0.0948 m, z = 0.2651 m ${\theta}_{x}$$=5\text{}\mathrm{deg},\text{}{\theta}_{y}$$={\theta}_{z}$= 0 |

Parameter | Value |
---|---|

Population size | 50 |

Maximum generations | $100$ the number of design variables |

Creation function | Random initial population satisfying bounds and linear constraints |

Mutation function | Mutation Adapt Feasible |

Selection function | Stochastic Uniform |

Crossover function | CrossoverIntermediate (weighted average of the parents) |

Crossover fraction | 0.8 |

Elite count | 3 |

Function tolerance | $1\times {10}^{-6}$ |

Constraint tolerance | $1\times {10}^{-3}$ |

Maximum stall generations | 50 |

Maximum stall time | $\infty $ |

Maximum time | $\infty $ |

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## Share and Cite

**MDPI and ACS Style**

Rosyid, A.; Stefanini, C.; El-Khasawneh, B.
A Reconfigurable Parallel Robot for On-Structure Machining of Large Structures. *Robotics* **2022**, *11*, 110.
https://doi.org/10.3390/robotics11050110

**AMA Style**

Rosyid A, Stefanini C, El-Khasawneh B.
A Reconfigurable Parallel Robot for On-Structure Machining of Large Structures. *Robotics*. 2022; 11(5):110.
https://doi.org/10.3390/robotics11050110

**Chicago/Turabian Style**

Rosyid, Abdur, Cesare Stefanini, and Bashar El-Khasawneh.
2022. "A Reconfigurable Parallel Robot for On-Structure Machining of Large Structures" *Robotics* 11, no. 5: 110.
https://doi.org/10.3390/robotics11050110