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JMST Advances

, Volume 1, Issue 1–2, pp 31–39 | Cite as

Analysis of the effect of system parameters for combined nonlinear cable elongation characteristics in CDPR

  • Sung-Hyun Choi
  • Kyoung-Su ParkEmail author
Letter
  • 100 Downloads

Abstract

The polymer cable is a widely used material in the cable-driven parallel robot (CDPR) system because of its many advantages such as high sensitivity, large workspace and so on. However, the accurate control of CDPR is not easy because of complicated response of the cable. In our previous study, the integrated cable model was derived. Based on the model, parametric studies were progressed in this paper. While operating CDPR, various parameters such as length, applied tension, and tensile rate can be changed and dominantly affect the dynamics of CDPR. For this reason, parametric study was based on these parameters. In this investigation, dynamic creep, hardening factor and short-term recovery were saturated as processing cyclic load. Each saturation rate was dominantly influenced by cable length and applied tension. As the tensile rate was increased, the dynamic creep was decreased. The hysteresis was the characteristic combining all of dynamics. So, the hysteresis also had saturation trends. When the exerted tension was decreased, the length of cable could be reduced or elongated because the creep and recovery occur at the same time.

Keywords

Dynamic creep Hardening effect Integrated nonlinear dynamic model Short- and long-term recovery 

1 Introduction

Cable-driven parallel robots (CDPRs) are operated by 8 cables connected with actuators (see Fig. 1). In recent years, CDPRs have become popular due to their advantages such as high sensitivity to movement, ease of maintenance and large workspace compared to the conventional rigid link robot [1, 2] even though the system has some nonlinear elongations due to cables. The polymer cables are widely used in CDPR systems because of its low weight and inertia. However, polymer cable has nonlinear and complex characteristics that greatly affect the actual cable length such as creep, hardening effect, hysteresis, short- and long- term recovery [3, 4]. These characteristics cause the change of cable length and it directly makes the pose error of CDPR. To identify the nonlinear characteristics of cable, many studies have been conducted [5, 6]. But, these researches considered not the integrated and combined nonlinear characteristic of cable but only the individual cable characteristic. As mentioned above, these nonlinear characteristics of cable is revealed as the combination of the cable characteristics as well as the characteristics interactively affect each other. So, we derived and verified an integrated dynamic model of cable based on a visco-elastic model in our previous study [6]. Also, while operating CDPR, various system parameters such as length, tension, tensile rate and so on can be changed. Among them, cable length, applied tension and tensile rate are the most dominant and the most changed factors. In the actual CDPRs, the tension applied to the cable usually varies from 2 to 150 N, depending on the system [7, 8] and the cable length can be changed in the operation. Also, since CDPR can be operated by various velocities and tensions, various tensile rates should be considered to consider the various industrial applications the CDPR. In our CDPR system, a normal operating velocity might be 200 mm/s. Thus, it is essential to analyze the effect of cable elongation for the various system parameters because the final length of the cable is needed accurately predicted.
Fig. 1

Cable-driven parallel robot

In this study, we conduct the parametric study to determine the nonlinear elongation of polymer cable for variations of the length, tension, and tensile rate. The dynamic model of the cable focuses on the hardening effects, dynamic creep, short- and long-term recovery, and hysteresis. In the first section of this paper, we describe the experiment and integrated nonlinear dynamic model. To investigate these characteristics, the cyclic load process is simulated for various samples and parameters because the nonlinear elongation of cable is sufficiently affected in the cyclic load. Next, we report the results of our parametric study under a range of conditions. To investigate the cable recovery characteristics, parametric study for short-term and long-term recovery is carried out by varying cable length, applied tension and recovery time. The effect of parameters for the hysteresis is evaluated with the cyclic process simulation. And, the combined cable nonlinear dynamics are evaluated while operating the arbitrary tension histories.

2 Experiment and characteristics of nonlinear cable elongation

2.1 Experimental setup

Because of the nonlinearity of our proposal cable model with respect to time, it is required to derive the loading, unloading time. To gain the finally applied loading and unloading time, we perform the cyclic loading test of the Dyneema polyethylene SK78 cable using a SHIMADZU AGS-X PLUS tensile tester. We applied tension from 50 to 150 N to the CDPR system. As the end-effector pose is changed, the cable length is also changed. Thus, it is necessary to perform under various length conditions. Therefore, we used the three kinds of cable lengths (100 mm, 200 mm and 300 mm). And, constant tensile rates are based on the 3 mm/min. Each test is repeated by three times and the mean values of the measurements are calculated.

2.2 Dynamic characteristics of polymer cable

The polymer cables used in CDPRs have the complex dynamic characteristics, including structural elongation, hysteresis, dynamic creep, and short- and long-term recovery. Each characteristic interacts with each other while operating CDPRs. The dynamics model was derived based on the visco-elastic model for time-dependent applied tension not static tension [6]. Also, the model considered the characteristic related to the dynamic creep phenomenon induced by the time-dependent tension variation. The strain is as follows:
$$\varepsilon_{i} (t) = \left( {\frac{{F_{\text{f}} }}{{E_{{ 1 , {\text{c}}}} A}}} \right)^{{h(\varepsilon_{i - 1} )}} - \frac{{F_{\text{f}} }}{{E_{1,r} A}}\, + \frac{{\int_{0}^{{t_{\text{total}} }} {F(t){\text{d}}t} }}{{t_{\text{total}} }}\left( {\frac{1}{{E_{{ 2 , {\text{c}}}} A}}\left( {1 - {\text{e}}^{{ - t_{\text{total}} /t_{\text{c}} }} } \right) + \frac{1}{{\eta_{0} A}} - \frac{1}{{E_{{ 2 , {\text{r}}}} A}}\left( {1 - {\text{e}}^{{ - t_{\text{total}} /t_{\text{r,1}} }} } \right)} \right),$$
(1)
$$\varepsilon_{i} (t) = \int_{0}^{{t_{\text{total}} }} {\dot{\varepsilon }_{i} (t){\text{d}}t} \approx \dot{\varepsilon }_{i} t_{\text{total}} \,({\text{for}}\,\,{\text{constant}}\,\,{\text{strain}}\,\,{\text{rate}}),$$
(2)
where Ff is currently applied tension, F means the tension over the time, E1,c and E2,c is the elastic parameter of elongation, E1,r and E2,r means elastic parameter of recovery, η0 is the Newtonian damping parameter for viscous behavior. Each parameter was described in detail and was verified in the [6]. The right-hand side first and second terms of Eq. (1) are related to structural elongation and short-term recovery. To describe the hardening of the cable caused by residual stress and continuous cyclic loads, the hardening factor h(ɛi − 1) was introduced. And the right-hand side integral term includes time-dependent dynamic creep and long-term recovery. However, it is difficult to solve the nonlinear dynamic equation for time-dependent applied tension. Therefore, we first did the cyclic test and additionally derived one more model for case of constant tensile rate (see Eq. 2). Because the visco-elastic model has nonlinearity with respect to the loading time ttotal, the actual time was derived using the Newton–Raphson method based on the condition that Eq. (1) is equal to Eq. (2) for constant tensile rate. After then, the dynamic strain in the loading and unloading cases could be derived using the predicted loading and unloading time:
$$\varepsilon_{{i - {\text{loading}}}} = \left( {\frac{{F_{\text{f}} }}{{E_{1} A}}} \right)^{{h(\varepsilon_{i - 1} )}} - \frac{{\int_{0}^{{t_{\text{total}} }} {F(t){\text{d}}t} }}{{t_{\text{total}} }}\left( {\frac{1}{{E_{2} A}}\left( {1 - e^{{ - t_{\text{total}} /t_{\text{c}} }} } \right) + \frac{1}{{\eta_{0} A}}} \right),$$
(3)
$$\varepsilon_{{i - {\text{unloading}}}} = \left( {\frac{{F_{\text{f}} }}{{E_{1} A}}} \right)^{{h(\varepsilon_{i - 1} )}} - \frac{{F_{\text{f}} }}{{E_{{ 1 , {\text{r}}}} A}} + \frac{{\int_{0}^{{t_{\text{total}} }} {F(t){\text{d}}t} }}{{t_{\text{total}} }}\left( {\frac{1}{{E_{2} A}}\left( {1 - {\text{e}}^{{ - t_{\text{total}} /t_{\text{c}} }} } \right) + \frac{1}{{\eta_{0} A}} - \frac{1}{{E_{{ 2 , {\text{r}}}} A}}\left( {1 - e^{{ - t_{\text{total}} /t_{\text{r,1}} }} } \right)} \right) - \frac{\Delta F}{{E_{{ 3 , {\text{r}}}} A}}\left( {1 - {\text{e}}^{{ - t_{\text{total}} /t_{\text{r,2}} }} } \right).$$
(4)
The equation contains all nonlinear elongation and recovery. The model is divided into two cases, which are loading and unloading process. In the case of loading operation, the elongation is caused by its structural stiffness and dynamic creep effect. A structural elongation has a linear characteristic. At the same time, dynamic creep occurs due to time-dependent force for a loading time. As the loading time is longer and the applied tension is larger, the dynamic creep has a logarithm form for the tension. In the case of unloading process, short-term recovery occurred in a moment as soon as the applied force is removed. It is also caused by structure of cable. Because of the unloading process, tension is gradually reduced. However, since there is still tension on the cable, dynamic creep occurs with short-term recovery simultaneously. If loading and unloading processes are repeated, the cable is hardened. So, the stiffness of cable is increased. In this process, the interactions of dynamic creep, short-term recovery and hardening make the hysteresis behavior. If the cable has some tension for a long time after unloading, the residual stress in cable is gradually reduced. At the same time, the long-term recovery occurred to original cable length. In addition, long-term recovery leads the cable to return to its original length. The above-mentioned characteristics are dominantly dependent on the cable length, applied tension, and tensile rate. To do the simulation, the properties of cable were prepared as shown in Table 1 [6].
Table 1

Parameters for dynamic cable model

Parameters

Values

Parameters

Values

E 1,c

1.8 Gpa

E 1,r

3 Gpa

E 2,c

8.2 Mpa

E 2,r

8.0 × 102 Mpa

η 0

5.0 × 103 Gpa

E 3,r

6.0 × 102 Mpa

t c

62.5 s.

t r,1

1 s.

β

0.0035

λ 1

8.65 × 105

γ

3.83

λ 2

1.0 × 103

\(\dot{\varepsilon }\)

0.016%/s, 0.032%/s

0.048%/s, 0.064%/s

A

7.06 mm2

l

100 mm, 200 mm, 300 mm

F f

50 N, 100 N, 150 N

3 Integration of nonlinear cable behavior of system parameters

3.1 Analysis of dynamic creep

To investigate the dynamic creep, the numerical analysis is performed based on the ten times of cyclic loading trajectory as shown in Fig. 2. Figure 2a is the simulation result of elongation under cyclic loading according to the cable length, Fig. 2b is the same simulation according to various applied tensions for the cable length of 300 mm. The tensile rate conditions are used in all 3 mm/min in these simulations. The dynamic creep behavior can be determined with the elongation phenomenon at each loading cycle. That is because polymer cable is elongated by the combination between the dynamic creep and static elongation during the loading cycle and the static elongation is constant for the first loading cycle. To investigate the dynamic creep, the elongation at the maximum tension of each cycle is used.
Fig. 2

The cable elongation behavior under the cyclic loading at different cable lengths and applied tension: a different cable lengths, b different applied tensions

Figure 3a shows the accumulated dynamic creep at loading part as the cycle progresses for various cable lengths. Figure 3b shows the dynamic creep during unloading process of each cycle for various cable lengths. It is the value excluding structural elongation. In overall, the dynamic creep is saturated as progressing the loading cycle. It seems to be logarithm according to the loading cycle immediately. For the case of 100 mm and 200 mm, the dynamic creeps are saturated at 6th, 8th cycle, respectively. The length of 300 mm cable is continuously elongated as the cycle progresses. Thus, dynamic creep tends to saturate the cyclic loads progress, and saturate later as cable length is longer. This is because the longer cable length is, the larger amount of residual stress that can occur in the molecules. In case of unloading process, dynamic creep saturates fast compared to the loading case. It is because the creep that occurs during unloading also includes the previous loading time. This result means that the dynamic creep phenomenon disappears as the cyclic loading is carried out and its effect appears in only low cyclic number in CDPR system. If you use sufficient warming-up process before CDPR operates, the cable elongation induced by the dynamic creep can be ignored.
Fig. 3

Cable elongation variation according to the cycle number (for cable length of 100 mm, 200 mm and 300 mm): a loading parts, b unloading part

To investigate the effect of the applied tension for the dynamic creep, the simulation under cyclic load is also performed in various applied tensions as shown in Fig. 2b. Figure 4a shows the dynamic creep according to the loading cycle number under different applied tension. In the case of 150 N, the dynamic creep is saturated at the 5th cycle. However, in the case of applied tension of 50 N and 100 N, the dynamic creep occurs continuously even though the tension trajectory has been reached at 10th cycle. It is because of the loading time. As the applied tension increases, the loading time for dynamic creep also increases in the same tensile rate. This long loading time causes large dynamic creep because of time dependency. Another reason is residual creep. As the cyclic load progresses, polymer strands and core removes all residue space associated with the cable. Thereafter, strand tends to fail to return to its original state due to friction between the strands [9]. In case of 150 N, cable is sufficiently elongated in the cyclic loading process because of high tension and long loading time. But in the case of 100 N and 50 N, residual creep remains. Figure 4b shows the dynamic creep of unloading part at each cycle. As same with length analysis, the unloading parts show faster saturation because unloading dynamic creep includes loading time.
Fig. 4

Dynamic creep variation according to the cycle number (maximum tension of 50 N, 100 N and 150 N): a loading parts, b unloading part

Another factor that dominantly affects the dynamic creep is the tensile rate related to speed of CDPR operation. To investigate the effect of tensile rate, the simulation is carried out with various tensile rates (see Fig. 4). In the figure, the blue, green, red and purple lines mean the tensile rate of 0.016%/s, 0.032%/s 0.048%/s, 0.064%/s, respectively. The tension is exerted from 0 to 100 N in the case of cable length of 300 mm. The simulation result only contains the dynamic creep not structural elongation. Since dynamic creep has nonlinear characteristics with respect to time and force, it has a nonlinear form as shown in Fig. 5. At the tensile rate of 0.016%/s, the dynamic creep of 7.30 mm occurred at final tension (i.e., tension of 100 N) On the other hand, for the cases of 0.032%/s, 0.048%/s, and 0.016%/s dynamic creeps of 7.14 mm, 6.99 mm and 6.82 mm are occurred, respectively. Thus, as the tensile rate increases, the dynamic creep decreases linearly. In the case of high tensile rate, since the loading time to approaching at the final tension is shorter than that of low tensile rate, the time affecting the dynamic creep is also decreased. The phenomenon can be explained through Eq. 3. In Eq. 3, the dynamic creep is modeled with the integral function. As the result, less dynamic creep occurred at higher tensile rate.
Fig. 5

The dynamic creep histories according to various tensile rates (cable length of 300 mm)

3.2 Analysis of cable hardening

The cable hardening is dependent on the residual strain of the cable which generates by operating CDPR continuously. To investigate this characteristic, the cyclic loading operation with ten times is used for simulation like the case of dynamic creep. It is because the loading part of each cycle contains hardening effect. It can be determined from stiffness. The tensile rate conditions are all 3 mm/min. Figures 6 and 7 show the gradient of loading cycle (i.e., stiffness) as progressing the cycles To determine the stiffness, the averaged gradient was calculated linearly using the initial tension (0 N) and the final tensions (50, 100 and 150 N) because the gradient at each point represents the stiffness at the moment. In the simulation, as cable length is increased, the stiffness is decreased. And the stiffness saturate lately as cable is longer. It is because of its structure. The hardening effect is caused by the deformation of the molecular network as the cable goes beyond the linear elastic range [10]. As the cable is longer, the cable has more molecular networks. To deform many of these polymer networks, many loading histories are required. Thus, as cable length is longer, hardening occurs during the long loading history. And, as increasing the applied tension, there are no changes of stiffness compared with the case of length. This is because nonlinear elongation follows the hookean spring behavior. The small change of stiffness according to the tension comes from creep due to difference of loading time. As the cycle progresses, the stiffness increases and then saturates. It is because hardening effect is closely related to creep. As the creep progresses, the cable becomes hardened. And these two characteristics interact with each other. So, hardening effect has same tendency as dynamic creep.
Fig. 6

Cable stiffness variation according cycle number (length of 100 mm, 200 mm and 300 mm)

Fig. 7

Cable stiffness variation according cycle number (the maximum tensions of 50 N, 100 N and 150 N)

3.3 Analysis of short- and long-term recovery

When the unloading begins, short-term recovery starts and induces the strain to vary nonlinearly with the tension. We used cyclic loading simulation to investigate short-term recovery and long-term recovery. To determine the recovery, the recovered cable lengths from maximum tension (50, 100, and 150 N) to minimum tension (0 N) in the loading cycle are investigated. Table 2 shows the short- and long-term recovery under the different various applied tensions. Dynamic creep is excluded from each value; and Table 3 is under the different cable length conditions. In the simulation, short- and long-term recovery tend to decrease as the cycle progresses, and finally saturated. In the long-term recovery, it is small enough to be ignored. This is because it is too short time for long-term recovery to occur. But short-term recovery is too large to ignore. In the case of short-term recovery, as increasing the applied tension, the saturation rate becomes faster. It is because of its relationship with structural elongation. Short-term recovery is the recovery of structural elongation [11]. Also, structural elongation contains the hardening effect. The hardening factor saturates as the cable length is shorter and the applied tension is higher. For this reason, short-term recovery has same tendency as hardening effect.
Table 2

The recovery according to the tension (cable length of 300 mm)

Cycle

1

2

3

4

5

Short-term recovery (mm)

 50 N

1.55

1.18

0.93

0.89

0.87

 100 N

1.92

1.46

1.15

1.12

1.10

 150 N

2.35

1.96

1.76

1.68

1.66

Long-term recovery (mm)

 50 N

0.024

0.020

0.020

0.016

0.016

 100 N

0.034

0.034

0.028

0.027

0.027

 150 N

0.041

0.038

0.035

0.031

0.030

Cycle

6

7

8

9

10

Short-term recovery (mm)

 50 N

0.86

0.86

0.85

0.85

0.85

 100 N

1.10

1.09

1.09

1.09

1.09

 150 N

1.66

1.66

1.66

1.66

1.66

Long-term recovery (mm)

 50 N

0.020

0.020

0.020

0.020

0.020

 100 N

0.027

0.027

0.027

0.027

0.027

 150 N

0.030

0.030

0.030

0.030

0.030

Table 3

The recovery according to the cable length (applied tension of 100 N)

Cycle

1

2

3

4

5

Short-term recovery (mm)

 100 mm

0.62

0.50

0.45

0.41

0.37

 200 mm

1.21

0.96

0.86

0.78

0.68

 300 mm

1.79

1.36

1.04

0.97

0.96

Long-term recovery (mm)

 100 mm

0.02

0.01

0.01

0.01

0.01

 200 mm

0.08

0.07

0.06

0.06

0.06

 300 mm

0.24

0.20

0.18

0.17

0.17

Cycle

6

7

8

9

10

Short-term recovery (mm)

 100 mm

0.35

0.35

0.35

0.35

0.35

 200 mm

0.66

0.66

0.66

0.66

0.66

 300 mm

0.96

0.96

0.95

0.95

0.94

Long-term recovery (mm)

 100 mm

0.01

0.01

0.01

0.01

0.01

 200 mm

0.06

0.06

0.06

0.06

0.06

 300 mm

0.170

0.170

0.170

0.170

0.170

3.4 Analysis of multi-combined effect of system parameters

As cable is exerted various tension, most of cable characteristics such as dynamic creep, hardening and short- and long-term recovery appear in integration. For example, in case of unloading, the cable length can increase or decrease depending on the loading history because of integrated characteristics. For this reason, the effective parameters in integrated loading situations are analyzed in this chapter. Firstly, hysteresis is investigated in the periodic cyclic loads. Hysteresis is caused by interactions between dynamic behaviors such as dynamic creep, hardening and short- and long-term recovery in periodic cyclic load. The loading part of hysteresis is caused by dynamic creep and the hardening effect, and the unloading part is caused by dynamic creep and short-term recovery. For this reason, the hysteresis reflects the characteristics of the total dynamic behavior in periodic cyclic load. Thus, the accuracy of the hysteresis determines the accuracy of the entire model in periodic cyclic load. We investigated the hysteresis behavior in terms of energy dissipation, which is the same as the area of the hysteresis. The hysteresis is investigated based on the cyclic load as shown in Fig. 2. Table 4 shows the energy dissipation with respect to the cyclic load for different lengths of cable. The energy dissipation decreased and then, also saturated. The decreasing trend of energy dissipation is due to the occurrence of residual stress, which reduces the amount of stretching. If all of the residual stress occurs, the hysteresis saturates to the completely one cycle. Table 5 is energy dissipation of hysteresis in different applied tension conditions. Like dynamic creep behavior according to the maximum tension, as the maximum tension increases, the saturation speed of energy dissipation increases. In other words, it has the similar tendency to dynamic creep because the hysteresis occurs due to dynamic creep and recovery.
Table 4

Energy dissipation of the hysteresis according to the cable length (maximum tension of 100 N)

Cycle

1

2

3

4

5

Hysteresis energy dissipation (J)

 100 mm

0.250

0.092

0.084

0.076

0.070

 200 mm

0.522

0.151

0.124

0.112

0.100

 300 mm

0.777

0.226

0.184

0.170

0.150

Cycle

6

7

8

9

10

Hysteresis energy dissipation (J)

 100 mm

0.067

0.063

0.062

0.060

0.060

 200 mm

0.093

0.087

0.086

0.086

0.086

 300 mm

0.149

0.141

0.138

0.138

0.138

Table 5

Energy dissipation of the hysteresis according to the tension (cable length of 300 mm)

Cycle

1

2

3

4

5

Hysteresis energy dissipation (J)

 50 N

0.135

0.119

0.110

0.099

0.090

 100 N

0.777

0.226

0.184

0.170

0.150

 150 N

1.360

0.450

0.375

0.345

0.340

Cycle

6

7

8

9

10

Hysteresis energy dissipation (J)

 50 N

0.086

0.082

0.082

0.082

0.082

 100 N

0.149

0.141

0.138

0.133

0.129

 150 N

0.331

0.322

0.322

0.322

0.322

Figure 8 is the test under various loading trajectories using 200 mm of cable. First, tension of 100 N was applied for 100 s in the tensile rate of 50 mm/min. And then, the load is decreased to an arbitrary load. The red, blue green and green lines mean the case of 25 N, 50 N and 75 N, respectively. In the graph, the creep has different form by the loading history. The case of second tension of 75 N, the elongated cable length decreases and then increases (forward creep). If the second tension is less than 75 N, the cable will slowly recover (backward creep) [12]. This phenomenon occurs because a short-term recovery occurs at the same time with creep. The most effective characteristics in the unloading process are creep and short-term recovery. If creep occurs more than short-term recovery, the cable is elongated. In contrast, if short-term recovery is larger than creep, recovery occurs. In case of 75 N, since the change in tension is only 25 N or less, it is greatly affected by creep. From this tendency, it can be predicted that the creep occurred more effectively if currently applied tension is near maximum tension (tension of 100 N).
Fig. 8

Investigation of cable dynamics in the arbitrary tension trajectory

Figure 9 shows the simulation in more complex tension trajectory by combining dynamic and static model of cable. The cable length condition is 300 mm. In the graph, the black dot line (process ①) means the dynamic creep, red dot line (process ②) is the static creep based on the Burger’s creep model [13, 14]. Blue line (process ③) is the short-term recovery combined with dynamic creep, and green line is the long-term recovery. In the profile, the tension is applied to the cable at a rate of 3 mm/min up to 100 N. After then, the cable maintains at 100 N for 60 s, and then, the cable is unloaded to 50 N and maintain for 60 s. Then, cable is unloaded by 0 N, and maintains the rest state for 2 days in the 0 N. Finally, one time of cyclic load is exerted by 3 mm/min. As the result of simulation, the creep of 5.8 mm occurred finally even though the long-term recovery had occurred. Also, the strain occurred by irregular form according to the tension trajectory. From these results, it is confirmed that the cable dynamics occurred by complex phenomena. Therefore, it should be an integrated model, not simply an individual model.
Fig. 9

Elongation profile for the combined tension histories

4 Conclusions

In this paper, we investigated the nonlinear dynamics behavior according to the various properties using the verified model. The dynamic behavior of cable was largely divided into four parts: hardening effect, dynamic creep, short- and long-term recovery, and hysteresis. To investigate the dynamic behavior, the effect of the parameters on the model was investigated. For the parameter study, various tensile rate, cable length and applied tension conditions were used. At first, dynamic creep behavior was investigated. Dynamic creep was saturated by one value as processing the cyclic load. The saturation rate was inversely proportional to the cable length, and proportional to the applied tension. Another factor that determines the dynamic creep was the tensile rate. The simulation is performed at the tension from 0 to 100 N. As the tensile rate increases, the dynamic creep decreases linearly. And, the short- and recovery was investigated based on the cyclic load. As increasing the applied tension, short-term recovery had fast the saturation rate. Moreover, In order to consider the CDPR characteristics in which various tension changes occur, the cable elongation characteristics in cyclic load and arbitrary trajectory were investigated. Because the hysteresis is result of cyclic loading, the characteristics were investigated for integrated characteristics. The hysteresis was the characteristics combining all of dynamic behavior such as dynamic creep, hardening short and long-term recovery. So, the model had same tendency as dynamic creep and hardening. And based on the model, the elongation was predicted in arbitrary tension trajectory. All of cable characteristics were affected by tension history. In particular, when the exerted tension was decreased, the length of the cable could be reduced or elongated because creep and recovery occur at the same time. As mentioned above, the elongation characteristics of the cable are very complex because they occur in a complex form. Therefore, predicting cable characteristics from the analysis of the effects of physical parameters is essential for accurate control of cable-driven parallel robots.

Notes

Acknowledgements

This research was supported by Development of Space Core Technology Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT and Future Planning (2017M1A3A3A02016340) and Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (20174030201530).

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Copyright information

© The Korean Society of Mechanical Engineers 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringGachon UniversitySeongnam-siKorea

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