# Kinematics and Dynamics Analysis of a 3-DOF Upper-Limb Exoskeleton with an Internally Rotated Elbow Joint

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## Abstract

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## Featured Application

**The proposed non-anthropomorphic 3-DOF upper-limb exoskeleton is appropriate for the purpose of material hanging in an industrial setting, especially for handling heavy loads by the front side of the human body.**

## Abstract

## 1. Introduction

## 2. Mechanism

#### 2.1. Principle of the 5-DOF Upper-Limb Exoskeleton

#### 2.2. Principle of the 3-DOF Upper-Limb Exoskeleton

#### 2.3. Differences Analysis

- There is an angle $\alpha $ between the forearm of the exoskeleton and the sagittal plane, as shown in Figure 4a. This results in the relative rotation between the end-effector and the hand. When the flexion of the elbow joint of the human body is at a maximum, the angle of the relative rotation between the end-effector and the hand is $53\xb0$. Since the movements of the end-effector under the control of the human are continuous and smooth, angle $\alpha $ does not affect the manipulability of the exoskeleton. This will be verified by the experiment in Section 5.
- The length of the human upper arm and forearm refer to human dimensions of Chinese adults, which is the National Standard of the People’s Republic of China, as shown in Figure 4b. There is an angle $\beta $ between the human forearm and the plane formed by the upper-arm and forearm of the exoskeleton. This results in ulnar deviation in the human wrist. When the elbow flexion of human body is at a maximum, the ulnar deviation is $54\xb0$. The maximum ulnar deviation allowed by the physiological structure is $55\xb0$ [23], which is greater than angle $\beta $. Therefore, ulnar deviation $\beta $ does not affect the manipulation of the exoskeleton.

#### 2.4. Singularity Analysis

## 3. Kinematic Analysis

#### 3.1. Forward Kinematics Analysis of the 5-DOF Upper-Limb Exoskeleton

#### 3.2. Inverse Kinematics Analysis of the 3-DOF Upper-Limb Exoskeleton

## 4. Dynamics Analysis

#### 4.1. Joint Trajectories

#### 4.2. Dynamics

## 5. Experiment

#### 5.1. Posture Analysis

#### 5.2. Motion Analysis

- Starting from the body side, remove the load from the lower hook, hang the load on the upper hook, and replace the exoskeleton prototype back to the body side.
- Starting from the body side, remove the load from the upper hook, hang the load on the lower hook, and replace the exoskeleton prototype back to the body side.

## 6. Conclusions

- The proposed 3-DOF exoskeleton had a reduced self-weight by removing two joints, and their corresponding actuators and eliminated singularity in the workspace. In addition, it is not necessary to avoid singularity in the workspace by means of rotating the base coordinate axis or the design of redundant degrees of freedom.
- The kinematics and dynamics analysis showed that the 3-DOF upper-limb exoskeleton had the same actual workspace as the 5-DOF upper-limb exoskeleton; compared with the 5-DOF upper-limb exoskeleton, the maximum joint torque of the 3-DOF upper-limb exoskeleton decreased by 50%, and the elbow external-flexion/internal-extension and the shoulder flexion/extension power consumption decreased by 55% and 46%, respectively, which will further reduce the exoskeleton weight.
- The experimental results showed that the angle $\alpha $ between the forearm of the 3-DOF upper-limb exoskeleton and the sagittal plane and the ulnar deviation $\beta $ had no influence on operating tasks; therefore, the proposed 3-DOF upper-limb exoskeleton with an internally rotated elbow joint had the same manipulability as the 5-DOF upper-limb exoskeleton for the hanging action process.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 2.**(

**a**) The model of the 5-DOF upper-limb exoskeleton; and (

**b**) The 5-DOF upper-limb exoskeleton.

**Figure 4.**Working configuration of the 3-DOF upper-limb exoskeleton. (

**a**) Top view; and (

**b**) right view.

**Figure 5.**Distance between the end-effector and shoulder joint: (

**a**) 5-DOF upper-limb exoskeleton; and (

**b**) 3-DOF upper-limb exoskeleton.

**Figure 7.**The workspace of the right arm of the 5-DOF upper-limb exoskeleton (mm): (

**a**) Isometric view; and (

**b**) right view.

Motion | Range |
---|---|

Shoulder flexion (Flex.)/extension (Ext.) $\left({Z}_{2}\right)$ | 180°/50° |

Shoulder adduction (Add.)/abduction (Abd.) $\left({Z}_{3}\right)$ | 180°/0° |

Shoulder internal (Int.)/external-rotation (Ext. Rot) $\left({Z}_{1}\right)$ | 90°/90° |

Elbow flexion (Flex.)/extension (Ext.) $\left({Z}_{4}\right)$ | 0°/145 |

Palmar flexion/dorsiflexion $\left({Z}_{6}\right)$ | 90°/70° |

Ulnar deviation/radial deviation $\left({Z}_{7}\right)$ | 55°/25° |

Wrist pronation (Pron.)/supination (Sup.) $\left({Z}_{5}\right)$ | 90°/90° |

Motion | Range |
---|---|

Shoulder Flex./Ext. $\left({\theta}_{2}^{5}\right)$ | 135°/15° |

Shoulder Add./Abd. $\left({\theta}_{1}^{5}\right)$ | 90°/30° |

Shoulder Int./Ext. Rot $\left({\theta}_{3}^{5}\right)$ | 90°/30° |

Elbow Flex./Ext. $\left({\theta}_{4}^{5}\right)$ | 118°/0° |

Elbow Pron./Sup. $\left({\theta}_{5}^{5}\right)$ | 30°/30° |

Motion | Function |
---|---|

Shoulder Flex./Ext. $\left({\theta}_{2}^{5}\right)$ | Complete lifting, pull down, etc., which require the upper-limb to swing back and forth. |

Shoulder Add./Abd. $\left({\theta}_{1}^{5}\right)$ | Complete side lifting, etc., which require the upper-limb to swing lateral. |

Shoulder Int./Ext. Rot $\left({\theta}_{3}^{5}\right)$ | Increase the workspace of the upper-limb. |

Elbow Flex./Ext. $\left({\theta}_{4}^{5}\right)$ | Complete lifting, pull down, etc., which require the upper-limb to swing back and forth. |

Elbow Pron./Sup. $\left({\theta}_{5}^{5}\right)$ | Increase the flexibility of the end-effector. |

Configration | Motion | Range |
---|---|---|

3-DOF | Shoulder Flex./Ext. $\left({\theta}_{1}^{3}\right)$ | 180°/50° |

Shoulder Add./Abd. $\left({\theta}_{2}^{3}\right)$ | 180°/30° | |

Elbow EF/IE $\left({\theta}_{3}^{3}\right)$ | 118°/0° |

Links | ${\mathit{\alpha}}_{\mathit{i}}$ | ${\mathit{a}}_{\mathit{i}}$ | ${\mathit{\theta}}_{\mathit{i}}^{5}$ | ${\mathit{d}}_{\mathit{i}}$ |
---|---|---|---|---|

1 | 0° | 0 | ${\theta}_{1}^{5}$ | 0 |

2 | −90° | ${a}_{2}$ | ${\theta}_{2}^{5}$ | 0 |

3 | −90° | 0 | ${\theta}_{3}^{5}$ | ${d}_{3}$ |

4 | −90° | 0 | ${\theta}_{4}^{5}$ | 0 |

Links | ${\mathit{\alpha}}_{\mathit{i}}$ | ${\mathit{a}}_{\mathit{i}}$ | ${\mathit{\theta}}_{\mathit{i}}^{3}$ | ${\mathit{d}}_{\mathit{i}}$ |
---|---|---|---|---|

1 | 0 | 0 | ${\theta}_{1}^{3}$ | 0 |

2 | −90° | ${a}_{2}$ | ${\theta}_{2}^{3}$ | 0 |

3 | 0 | ${a}_{3}$ | ${\theta}_{3}^{3}$ | 0 |

Motion | Motion Range | |
---|---|---|

Inverse Kinematics Extremum | Range | |

${\theta}_{1}^{3}$ | 90°/−105° | 180°/15° |

${\theta}_{2}^{3}$ | 29°/−104° | 29°/104° |

${\theta}_{3}^{3}$ | 123°/12° | 123°/12° |

Action | Parameters | Data |
---|---|---|

Raising up | ${O}_{0}{G}_{0}$ | 1500 mm |

${B}_{0}{B}_{0}^{\prime}$ | 883 mm | |

${B}_{1}{B}_{1}^{\prime}$ | 1931 mm | |

Lateral lifting | ${O}_{0}{B}_{0}^{\prime}$ | 1500 mm |

${B}_{0}^{\prime}{B}_{1}^{\prime}$ | 350 mm | |

$\angle {B}_{0}{O}_{0}{B}_{1}$ | 30° |

Configration | Motion | Maximum Joint Torque (Nm) |
---|---|---|

5-DOF | Shoulder Flex./Ext. $\left({\theta}_{1}^{5}\right)$ | 295 |

Shoulder Add./Abd. $\left({\theta}_{2}^{5}\right)$ | 185 | |

Shoulder Int./Ext. Rot $\left({\theta}_{3}^{5}\right)$ | 0 | |

Elbow Flex./Ext. $\left({\theta}_{4}^{5}\right)$ | 192 | |

Elbow Pron./Sup. $\left({\theta}_{5}^{5}\right)$ | 0 | |

3-DOF | Shoulder Flex./Ext. $\left({\theta}_{1}^{3}\right)$ | 295 |

Shoulder Add./Abd. $\left({\theta}_{2}^{3}\right)$ | 185 | |

Elbow EF/IE $\left({\theta}_{3}^{3}\right)$ | 96 |

Configration | Motion | Maximum Joint Power Consumption (W) |
---|---|---|

3-DOF | Shoulder Flex./Ext. $\left({\theta}_{1}^{3}\right)$ | 113.3 |

Shoulder Add./Abd. $\left({\theta}_{2}^{3}\right)$ | 3.4 | |

Elbow EF/IE $\left({\theta}_{3}^{3}\right)$ | 68.3 | |

5-DOF | Shoulder Flex./Ext. $\left({\theta}_{1}^{5}\right)$ | 210.4 |

Shoulder Add./Abd. $\left({\theta}_{2}^{5}\right)$ | 0 | |

Shoulder Int./Ext. Rot $\left({\theta}_{3}^{5}\right)$ | 0 | |

Elbow Flex./Ext. $\left({\theta}_{4}^{5}\right)$ | 153.4 |

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**MDPI and ACS Style**

Wang, X.; Song, Q.; Wang, X.; Liu, P. Kinematics and Dynamics Analysis of a 3-DOF Upper-Limb Exoskeleton with an Internally Rotated Elbow Joint. *Appl. Sci.* **2018**, *8*, 464.
https://doi.org/10.3390/app8030464

**AMA Style**

Wang X, Song Q, Wang X, Liu P. Kinematics and Dynamics Analysis of a 3-DOF Upper-Limb Exoskeleton with an Internally Rotated Elbow Joint. *Applied Sciences*. 2018; 8(3):464.
https://doi.org/10.3390/app8030464

**Chicago/Turabian Style**

Wang, Xin, Qiuzhi Song, Xiaoguang Wang, and Pengzhan Liu. 2018. "Kinematics and Dynamics Analysis of a 3-DOF Upper-Limb Exoskeleton with an Internally Rotated Elbow Joint" *Applied Sciences* 8, no. 3: 464.
https://doi.org/10.3390/app8030464