# Estimation of 1-Repetition Maximum Using a Hydraulic Bench Press Machine Based on User’s Lifting Speed and Load Weight

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Method

#### 2.2. Experiment Methods

#### 2.2.1. Subject

#### 2.2.2. Experimental Design

## 3. Results

#### 3.1. Comparison between Plate and Hydraulic 1RMs

#### 3.2. RM Equation

## 4. Discussion

#### 4.1. Comparison between Plate and Hydraulic 1RM Equations

#### 4.2. Advantages of Using Hydraulic Fitness Machines

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) A hydraulic cylinder and a step motor were connected to a conventional bench press machine. Instead of weight plates, hydraulic pressure from the cylinder acted as load weight to the machine; (

**b**) As the dial indicator increases, the load weight almost linearly increases. The extending speed of the cylinder rod affects the load weight as well; (

**c**) The flow chart summarizes the 1RM measurement process using the hydraulic press machine.

**Figure 2.**The handle position of the bench press machine during lifting exercises with the dial indicator of (

**a**) 1, (

**b**) 3.11, (

**c**) 5.35. If the chest press exercise is successful and fast, the dial indicator of hydraulic cylinder valve increases and suggests heavier load weight until the lifting speed naturally decreases and the load weight reaches 1RM.

**Figure 3.**1RM measured using conventional press machine (plate 1RM) and 1RM measured using hydraulic press machine (hydraulic 1RM). Mean hydraulic 1RM represents the average of the three paired hydraulic 1RMs.

**Figure 4.**Goodness-of-fit of the two 1RM equations’ load weight $W$ and lifting speed $v$: (

**a**) $1\mathrm{RM}=-14.8408+0.8644W+0.6040v-0.0039{v}^{2}$; (

**b**) $1\mathrm{RM}=-0.3908+0.8251W+0.1054v$.

**Figure 5.**Non-1RM data points and 1RM decision boundaries based on the equation, $1\mathrm{RM}=-0.3908+0.8251W+0.1054v$. The color of each data point indicates the actual 1RM.

**Figure 7.**Non-1RM data points and 1RM decision boundaries based on the equations from reference papers: (

**a**) $v=-1.46\times \frac{W}{1\mathrm{RM}}+1.7035$; (

**b**) $\frac{W}{1\mathrm{RM}}\times 100=7.5786{v}^{2}-75.865v+113.02$. The color of each data point indicates the actual 1RM.

Measure | Mean Square | F | Significance ^{b} |
---|---|---|---|

1RM | 165.589 | 5.709 | 0.009 |

^{b}Greenhouse–Geisser correction was used because of non-sphericity.

Measure 1 | Measure 2 | Mean Difference | Standard Error | Significance ^{b} | 95% Confidence | |
---|---|---|---|---|---|---|

Lower | Upper | |||||

plate 1RM | hydraulic 1RM (1) | 1.445 | 0.829 | 0.566 | −0.939 | 3.829 |

hydraulic 1RM (2) | −1.832 | 1.086 | 0.628 | −4.956 | 1.291 | |

hydraulic 1RM (3) | −2.946 | 0.982 | * 0.037 | −5.769 | −0.123 | |

hydraulic 1RM (1) | hydraulic 1RM (2) | −3.277 | 0.829 | * 0.004 | −5.660 | −0.894 |

hydraulic 1RM (3) | −4.390 | 1.295 | * 0.014 | −8.113 | −0.667 | |

hydraulic 1RM (2) | hydraulic 1RM (3) | −1.113 | 1.659 | 1.000 | −5.883 | 3.656 |

^{b}Adjustment for multiple comparisons: Bonferroni.

Mean | Standard Deviation | Standard Error Mean | 95% Confidence | t | df | Significance (2-Tailed) | ||
---|---|---|---|---|---|---|---|---|

Lower | Upper | |||||||

plate 1RM—mean hydraulic 1RM | −1.11120 | 3.06384 | 0.585 | −2.37589 | 0.15349 | −1.813 | 24 | 0.082 |

Model | Parameter | Order | Coefficient | p-Value | Residual Standard Error | Adjusted R-Squared |
---|---|---|---|---|---|---|

1 | Intercept | −13.965266 | * 0.03552 | 2.969 | 0.8995 | |

Load weight, $W$ (kg) | 1 | 0.703188 | ** 0.00261 | |||

2 | 0.003117 | 0.42045 | ||||

Lifting speed, $v$ (mm/s) | 1 | 0.630198 | ** 0.00427 | |||

2 | −0.004075 | * 0.01379 | ||||

2 | Intercept | −14.840838 | * 0.02308 | 2.946 | 0.901 | |

Load weight, $W$ (kg) | 1 | 0.864368 | *** 0.00000 | |||

Lifting speed, $v$ (mm/s) | 1 | 0.603973 | ** 0.00478 | |||

2 | −0.003890 | * 0.01578 | ||||

3 | Intercept | −0.39076 | 0.89201 | 3.317 | 0.8745 | |

Load weight, $W$ (kg) | 1 | 0.82505 | *** 0.00000 | |||

Lifting speed, $v$ (mm/s) | 1 | 0.10540 | ** 0.00113 |

Count | 1RM (kg) | Total | |||||
---|---|---|---|---|---|---|---|

(10, 20) | (20, 30) | (30, 40) | (40, 50) | (50, 60) | |||

Lifting speed (mm/s) | (100, 120) | 4 | 3 | 1 | 0 | 1 | 9 |

(80, 100) | 6 | 7 | 1 | 1 | 0 | 15 | |

(60, 80) | 11 | 10 | 9 | 3 | 1 | 34 | |

(40, 60) | 5 | 9 | 2 | 1 | 0 | 17 | |

Total | 26 | 29 | 13 | 5 | 2 | 75 |

1RM Error | N | Mean | Standard Deviation | Standard Error | 95% Confidence | Minimum | Maximum | |
---|---|---|---|---|---|---|---|---|

Lower | Upper | |||||||

Equation (4) | 25 | −0.572 | 2.726 | 0.545 | −1.697 | 0.553 | −4.95 | 6.42 |

Equation (5) | 25 | 5.024 | 2.392 | 0.478 | 4.037 | 6.012 | 1.62 | 10.75 |

Equation (6) | 25 | 4.208 | 2.299 | 0.460 | 3.259 | 5.157 | 0.52 | 9.32 |

**Table 7.**The load weight, the number of reps for a set, the number of sets and break time depending on the exercising type [7].

Exercising Type | Load Weight | Reps for a Set | The Number of Sets | Break Time per Set |
---|---|---|---|---|

Muscular exercise | Above 85% of 1RM | Under 6 reps | 2–6 sets | 2–5 min |

Muscular hypertrophy exercise | About 67–85% of 1RM | 6–12 reps | 3–6 sets | 30–90 s |

Muscle endurance exercise | Below 67% of 1RM | Over 12 reps | 2–3 sets | 30 s |

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**MDPI and ACS Style**

Yoo, J.; Kim, J.; Hwang, B.; Shim, G.; Kim, J.
Estimation of 1-Repetition Maximum Using a Hydraulic Bench Press Machine Based on User’s Lifting Speed and Load Weight. *Sensors* **2022**, *22*, 698.
https://doi.org/10.3390/s22020698

**AMA Style**

Yoo J, Kim J, Hwang B, Shim G, Kim J.
Estimation of 1-Repetition Maximum Using a Hydraulic Bench Press Machine Based on User’s Lifting Speed and Load Weight. *Sensors*. 2022; 22(2):698.
https://doi.org/10.3390/s22020698

**Chicago/Turabian Style**

Yoo, Jinyeol, Jihun Kim, Byunggon Hwang, Gyuseok Shim, and Jaehyo Kim.
2022. "Estimation of 1-Repetition Maximum Using a Hydraulic Bench Press Machine Based on User’s Lifting Speed and Load Weight" *Sensors* 22, no. 2: 698.
https://doi.org/10.3390/s22020698