Articulated manipulator with descending link mass

In the subsequent stages, if the specific parameters are determined that the mass of

each link is half as heavy as the preceding link owing to the strength requirement of the

manipulator as displayed in Eq. (29a), and that all link lengths are equal to each other as

shown in Eq. (29b), and that all mass centers are located in the middle point of

corresponding links as shown in Eq. (29c).

j j-1

m = m for j = 1, 2, , n

2 (29a)

r = r for j = 1, 2, j , n (29b)

j j

s 1

= for j = 1, 2, , n

r 2 (29c)

The quantitative efficiency index can be obtained following the aforementioned

processes. The magnitudes of gravitational energy contributions can be obtained, and the

magnitudes of elastic energy contributions is determined accordingly. The quantitative

efficiency index is obtained as the magnitude ratio of the positive elastic energy

contributions to the total elastic energy contributions and listed in Table 6.

Table 6

Quantitative efficiency index of five-link articulated manipulators with descending link mass

Among articulated manipulators with descending link mass, the quantitative

efficiency indexes of those with spring configuration matrices 5-1, 5-2 and 5-3 are the

highest. The quantitative efficiency index indicates the proportion of elastic energy

contributions that does assist in achieving static balance. Therefore, the change of

quantitative efficiency index from 0.6 to 0.7 suggests that the elastic energy wastes is

reduced from 40% to 30%. In the case that the attachment length ratio ρ are selected to

be 1, the quantitative efficiency indexes vary from 0.619 to 0.695. The possible energy

0 0 # 0 #

wastes can be reduced from 38.1% to 30.5% if the energy efficiency assessment method

is adopted during the design processes. In addition, quantitative efficiency indexes of the

five-link articulated manipulators with descending link mass are further illustrated and

compared in Fig. 9 respectively.

Fig. 9. Quantitative efficiency index of five-link articulated manipulators with descending link mass

Notice that the energy efficiency assessment results with quantitative efficiency

index could be different from those with qualitative efficiency index. In the demonstrated

example, the most energy efficient articulated manipulator is that with spring

configuration matrix 5-4 as the qualitative efficiency index method is adopted.

Nevertheless, the most energy efficient articulated manipulators are suggested to be those

Configurations 5-1, 5-2, 5-3

Configuration 5-5 Configuration 5-4

method is adopted under the assumption of both equal link mass and descending link

mass. The quantitative efficiency index is more accurate than the qualitative efficiency

index since the magnitudes of energy contributions are taken into consideration. However,

the qualitative efficiency index could be essential during the preliminary stages of a

mechanism design, which provides a roughly evaluation for the designer when the

specific properties of the mechanism is not ascertained.

In addition, if more constraints are applied for the spring attachment length ratios, it

is not necessary to assume that all selectable attachment length ratios to be the same value ρ. Some of the attachment length ratios of springs can be selected respectively according

to the specific constraints based on the designer’s requirements, and the quantitative

efficiency indexes of articulated manipulators with spring configuration 5-1, 5-2 and 5-3

could be further compared.

Chapter 7 Conclusions

A methodology to assess the energy efficiency of statically balanced articulated

manipulators with different spring configurations is proposed in this study. Spring

installation configurations are determined according to specific rules based on the

counteraction between gravitational and elastic potential energy expressed in the total

stiffness block matrix. Elastic energy contributions are identified to be negative or

positive contributions considering the direction properties that are aligned with or against

the gravitational energy contributions. In the case that the specific parameters of

articulated parameters are not given variables, the magnitudes of gravitational energy

contributions are unknown. A qualitative efficiency index is proposed for assessment of

the energy efficiency of the articulated manipulators with different spring configurations.

In the case that the parameters of articulated manipulators are given or selected under

some specific assumptions, the magnitudes of gravitational energy contributions can be

taken into consideration. A quantitative efficiency index is proposed for assessment of the

energy efficiency of the articulated manipulators with different spring configurations in a

more accurate way. The quantitative efficiency index indicates the proportion of elastic

quantitative efficiency index is, the better the energy efficiency the mechanism is. In

theory, it is expected to maximize the quantitative efficiency index; nevertheless, the

trade-off between energy efficiency and space saving has to be properly considered

according to requirements of each individual design. A design example is demonstrated

to illustrate the practical uses of the efficiency indexes proposed in this study. The

qualitative efficiency index can be applied during the preliminary stages of a mechanism

design, providing a roughly evaluation when the specific properties of the mechanism

remains uncertain. On the other hand, the quantitative efficiency index provides an

accurate energy efficiency assessment of the articulated manipulators if the properties of

the designated mechanism are taken into consideration. The methodology can be adopted

to help designers to compare the energy efficiency among different statically

spring-balanced mechanisms and obtain the most efficient one from energy perspective.

Reference

1. Lu, Q., Ortega, C., & Ma, O. (2011). Passive gravity compensation mechanisms:

technologies and applications. Recent Patents on Engineering, 5(1), 32-44.

2. French, M., & Widden, M. (2000). The spring-and-lever balancing mechanism, George Carwardine and the Anglepoise lamp. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 214(3), 501-508.

3. Brown, G., & DiGuilio, A. O. (1980). Support apparatus. Google Patents.

4. Saluja, R., & Nagare, A. T. (1991). Counterbalanced arm for a lighthead. Google Patents.

5. Bell, W. R., Coon, D. C., & Peterson, T. M. (2001). Support arm for surgical light apparatus. Google Patents.

6. Banala, S. K., Agrawal, S. K., Fattah, A., Krishnamoorthy, V., Hsu, W.-L., Scholz, J., et al. (2006). Gravity-balancing leg orthosis and its performance evaluation. IEEE transactions on robotics, 22(6), 1228-1239.

7. Lin, P.-Y., Shieh, W.-B., & Chen, D.-Z. (2013). A theoretical study of weight-balanced mechanisms for design of spring assistive mobile arm support (MAS). Mechanism and Machine Theory, 61, 156-167.

8. Dunning, A., & Herder, J. A close-to-body 3-spring configuration for gravity balancing of the arm. In 2015 IEEE International Conference on Rehabilitation Robotics (ICORR), 2015 (pp. 464-469): IEEE

9. Tseng, T.-Y., Hsu, W.-C., Lin, L.-F., & Kuo, C.-H. Design and Experimental Evaluation of a Reconfigurable Gravity-Free Muscle Training Assistive Device for Lower-Limb Paralysis Patients. In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, 2015 (pp. V05AT08A037-V005AT008A037): American Society of Mechanical Engineers

10. Simionescu, I., & Ciupitu, L. (2000). The static balancing of the industrial robot arms:

part i: discrete balancing. Mechanism and Machine Theory, 35(9), 1287-1298.

11. Simionescu, I., & Ciupitu, L. (2000). The static balancing of the industrial robot arms:

part II: continuous balancing. Mechanism and Machine Theory, 35(9), 1299-1311.

12. Liu, L., Huang, B., Zhu, Y. H., & Zhao, J. Optimization Design of Gravity

13. Arakelian, V. (2016). Gravity compensation in robotics. Advanced Robotics, 30(2), 79-96.

14. Wang, J., & Gosselin, C. M. (1999). Static balancing of spatial three-degree-of-freedom parallel mechanisms. Mechanism and Machine Theory, 34(3), 437-452.

15. Lessard, S., Bonev, I., Bigras, P., Briot, S., & Arakelyan, V. Optimum static balancing of the parallel robot for medical 3D-ultrasound imaging. In IFTOMM 2007:

12th World Congress in Mechanism and Machine Science, 2007

16. Nathan, R. (1985). A constant force generation mechanism. Journal of mechanisms, transmissions, and automation in design, 107(4), 508-512.

17. Rahman, T., Ramanathan, R., Seliktar, R., & Harwin, W. (1995). A simple technique to passively gravity-balance articulated mechanisms. Journal of Mechanical Design, 117(4), 655-658.

18. Agrawal, S. K., & Fattah, A. (2004). Gravity-balancing of spatial robotic manipulators.

Mechanism and Machine Theory, 39(12), 1331-1344.

19. Agrawal, S. K., & Fattah, A. (2004). Theory and design of an orthotic device for full or partial gravity-balancing of a human leg during motion. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 12(2), 157-165.

20. Fattah, A., & Agrawal, S. K. Gravity-balancing of classes of industrial robots. In Proceedings 2006 IEEE International Conference on Robotics and Automation, 2006. ICRA 2006., 2006 (pp. 2872-2877): IEEE

21. Deepak, S. R., & Ananthasuresh, G. Static balancing of spring-loaded planar revolute-joint linkages without auxiliary links. In 14th National Conference on Machines and Mechanisms, 2009 (pp. 17-18)

22. Deepak, S. R., & Ananthasuresh, G. (2012). Perfect static balance of linkages by addition of springs but not auxiliary bodies. Journal of mechanisms and robotics, 4(2), 021014.

23. Lin, P.-Y., Shieh, W.-B., & Chen, D.-Z. (2010). A stiffness matrix approach for the design of statically balanced planar articulated manipulators. Mechanism and Machine Theory, 45(12), 1877-1891.

24. Lin, P.-Y., Shieh, W.-B., & Chen, D.-Z. (2012). Design of statically balanced planar articulated manipulators with spring suspension. IEEE transactions on robotics, 28(1), 12-21.

25. Lee, Y.-Y., & Chen, D.-Z. (2014). Determination of spring installation configuration on statically balanced planar articulated manipulators. Mechanism and Machine Theory, 74, 319-336.

26. Sciavicco, L., & Siciliano, B. (2012). Modelling and control of robot manipulators:

Springer Science & Business Media.