Designing a Cross Trainer Using an Artificial Neural Network

  • Siddhartha Patra Jadavpur University


Cross-trainers are machines that use link mechanisms to mimic walking or running as part of workout sessions or rehabilitation systems. The simplest cross-trainer incorporates a crank-rocker or a crank-slider mechanism and provides a nearly elliptical path for foot motion. However, the natural human foot trajectories are far from being elliptical. Therefore, existing designs require modifications. Artificial neural networks are used for this purpose. Instead of trying to match the foot trajectory directly, here we tried to match different geometric properties of the area enclosed by the foot trajectory. Neural networks are trained to predict these geometric properties as outputs with the dimensions of the linkage as inputs. With the help of the same trained network, the “best-fit dimensions” were predicted for the desired trajectories.


cross-trainer, Artificial Neural Network, foot trajectory, optimization,


1. H. Schmidt, D. Sorowka, S. Hesse, R. Bemhardt, Development aspects of a robotised gait trainer for neurological rehabilitation, 2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, vol. 2, pp. 1340–1343, 2001, doi: 10.1109/IEMBS.2001.1020444.

2. R. Grasso, Y.P. Ivanenko, M. Zago, M. Molinari, G. Scivoletto, V. Castellano, V. Macellari, F. Lacquaniti, Distributed plasticity of locomotor pattern generators in spinal cord injured patients, Brain, 127(5): 1019–1034, 2004, doi: 10.1093/brain/awh115.

3. D.H.F. Chang, N.F. Troje, Acceleration carries the local inversion effect in biological motion perception, Journal of Vision, 9(1): 1–17, 2009, doi: 10.1167/9.1.19.

4. C. Shirota, A.M. Simon, T.A. Kuiken, Transfemoral amputee recovery strategies following trips to their sound and prosthesis sides throughout swing phase, Journal of NeuroEngineering and Rehabilitation, 12: 79 (12 pages), 2015, doi: 10.1186/s12984-015-0067-8.

5. R. Mendoza-Crespo, D. Torricelli, J.C. Huegel, J.L. Gordillo, J.L. Pons, R. Soto, An adaptable human-like gait pattern generator derived from a lower limb exoskeleton, Frontiers in Robotics and AI, 6 (36 pages), 2019, doi: 10.3389/frobt.2019.00036.

6. S.E. Park, Y.J. Ho, M.H. Chun, J. Choi, Y. Moon, Measurement and analysis of gait pattern during stair walk for improvement of robotic locomotion rehabilitation system, Analysis of Human Behavior for Robot Design and Control, 2019: 1495289 (12 pages), 2019, doi: 10.1155/2019/1495289.

7. H.S. Lee, Creative design of an elliptical trainer with two degrees of freedom, International Journal of Mechanical Engineering Education, 36(4): 284–293, 2008, doi: 10.7227/IJMEE.36.4.2.

8. C.A. Nelson, J.M. Burnfield, Y. Shu, T.W. Buster, A.P. Taylor, A. Graham, Modified elliptical machine motor-drive design for assistive gait rehabilitation, Journal of Medical Devices, 5(2): 021001 (7 pages), 2011, doi: 10.1115/1.4003693.

9. C.A. Nelson, J.M. Burnfield, Improved Elliptical Trainer Biomechanics Using a Modified Cardan Gear, [in:] Proceedings of the ASME 2012 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference IDETC/CIE, Chicago, IL, USA, 2012, doi: 10.1115/DETC2012-70439.

10. F.-C. Chen, Y.-F. Tzeng, W.-R. Chen, On the mechanism design of an innovative elliptical exerciser with quick return effect, International Journal of Engineering and Technology Innovation, 8(3): 228–239, 2018.

11. J.M. Burnfield, T.W. Buster, C.M. Pfeifer, S.L. Irons, G.M. Cesar, C.A. Nelson, Adapted motor-assisted elliptical for rehabilitation of children with physical disabilities, Journal of Medical Devices, 13(1): 011006 (9 pages), 2019, doi: 10.1115/1.4041588.

12. F.-C. Chen, Y.-F. Tzeng, M.-H. Hsu, Innovative design of an elliptical trainer with right timing of the foot trajectory, Advances in Technology Innovation, 5(3): 190–201, 2020, doi: 10.46604/aiti.2020.5645.

13. E. Hummer, E. Murphy, D.N. Suprak, L. Brilla, J.G. San Juan, The effects of a standard elliptical vs. a modified elliptical with a converging footpath on lower limb kinematics and muscle activity, Journal of Sports Sciences, 38(20): 2382–2389, 2020, doi: 10.1080/02640414.2020.1786241.

14. M.O. Shabani, A. Mazahery, The ANN application in FEM modeling of mechanical properties of Al-Si alloy, Applied Mathematical Modelling, 35(12): 5707–5713, 2011, doi: 10.1016/j.apm.2011.05.008.

15. A.K. Gupta, H.N. Krishnamurthy, Y. Singh, K.M. Prasad, S.K. Singh, Development of constitutive models for dynamic strain aging regime in Austenitic stainless steel 304, Materials and Design, 45: 616–627, 2013, doi: 10.1016/j.matdes.2012.09.041.

16. R.K. Desu, H.N. Krishnamurthy, A. Balu, A.K. Gupta, S.K. Singh, Mechanical properties of Austenitic Stainless Steel 304L and 316L at elevated temperatures, Journal of Materials Research and Technology, 5(1): 13–20, 2015, doi: 10.1016/j.jmrt.2015.04.001.

17. C.-W. Chang, H.-W. Lee, C.-H. Liu, A review of artificial intelligence algorithms used for smart machine tools, Inventions, 3: 41 (28 pages), 2018, doi: 10.3390/inventions3030041.

18. L.A. Ciro De Filippis, L.M. Serio, F. Facchini, G. Mummolo, ANN modelling to optimize manufacturing process, Advanced Applications for Artificial Neural Networks, A. El-Shahat [Ed.], vol. 11, pp. 201–225, 2018, doi: 10.5772/intechopen.71237.

19. N.K. Hong, S.-P. Chang, S.-C. Lee, Development of ANN-based preliminary structural design systems for cable-stayed bridges, Advances in Engineering Software, 33(2): 85–96, 2002, doi: 10.1016/S0965-9978(01)00057-6.

20. W.J.S. Gomes, A.T. Beck, Global structural optimization considering expected consequences of failure and using ANN surrogates, Computers and Structures, 126: 56–68, 2013, doi: 10.1016/j.compstruc.2012.10.013.

21. H. Mote, S.R.S. Kumar, Use of artificial neural network for initial design of steel, 2019 IOP Conference Series: Materials Science and Engineering, 660: 012064 (8 pages), 2019, doi: 10.1088/1757-899X/660/1/012064.

22. Y. Liu, The review of intelligent mechanical engineering based on artificial neural network, [in:] Proceedings of the 2015 International Conference on Intelligent Systems Research and Mechatronics Engineering, pp. 1969–1973, 2015, doi: 10.2991/isrme-15.2015.405.

23. F.S. Panchal, M. Panchal, Review on methods of selecting number of hidden nodes in artificial neural network, International Journal of Computer Science and Mobile Computing (IJCSMC), 3(11): 455–464, 2014.

24. T. Kavzoglu, S. Reis, Performance analysis of maximum likelihood and artificial neural network classifiers for training sets with mixed pixels, GIScience & Remote Sensing, 45(3): 330–342, 2008, doi: 10.2747/1548-1603.45.3.330.

25. A. Ng, One hidden layer. Neural Network. Computing a Neural Network’s Output, Standford University, [online], available:

26. G.E. Hinton, N. Srivastava, A. Krizhevsky, I. Sutskever, R.R. Salakhutdinov, Improving neural networks by preventing co-adaptation of feature detectors, arXiv:1207.0580, 2012.

27. G. Li, H. Alnuweiri, Y. Wu, H. Li, Acceleration of backpropagations through initial weight pre-training with delta rule, IEEE International Conference on Neural Networks, vol. 1, pp. 580–585, 1993, doi: 10.1109/ICNN.1993.298622.

28. X. Glorot, Y. Bengio, Understanding the difficulty of training deep feedforward neural networks, [in:] Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR, 9, pp. 249–256, Chia Laguna Resort, Sardinia, Italy, 2010,

29. J. Martens, I. Sutskever, Training deep and recurrent networks with Hessian-free optimization, [in:] Montavon G., Orr G.B., Müller K.R. [Eds], Neural Networks: Tricks of the Trade. Lecture Notes in Computer Science, vol. 7700, Springer, Berlin, Heidelberg, doi: 10.1007/978-3-642-35289-8_27.

30. I. Sutskever, J. Martens, G. Dahl, G. Hinton, On the importance of initialization and momentum in deep learning, [in:] Proceedings of the 30th International Conference on Machine Learning, PMLR, vol. 28(3), pp. 1139–1147, Atlanta, Georgia, USA, 2013,

31. B.T. Polyak, Some methods of speeding up the convergence of iteration methods, USSR Computational Mathematics and Mathematical Physics, 4(5): 1–17, 1964.

32. Y. Nesterov, A method for solving the convex programming problem with convergence rate O(1/k2), Soviet Mathematics Doklady, 27: 372–376, 1983.

33. Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course, vol. 87, Kluwer Academic Publishers, 2004.

34. L. Prechelt, Early stopping – But when?, [in:] Orr G.B., Müller K.-R. [Eds], Neural Networks: Tricks of the Trade. Lecture Notes in Computer Science, vol. 1524, pp. 55–69, Springer, Berlin, Heidelberg, 1998, doi: 10.1007/3-540-49430-8_3.

35. A.Y. Ng, Feature selection, L1 vs. L2 regularization, and rotational invariance, [in:] ICML ’04: Proceedings of the Twenty-First International Conference on Machine Learning, 78 pages, Banff, Canada, July 2004, doi: 10.1145/1015330.1015435.

36. Z. Lian, X. Jing, X.Wang, H. Huang, Y. Tan, Y. Cui, DropConnect regularization method with sparsity constraint for neural networks, Chinese Journal of Electronics, 25(1): 152–158, 2016, doi: 10.1049/cje.2016.01.023.

37. L. Wan, M. Zeiler, S. Zhang, Y. Le Cun, R. Fergus, Regularization of neural networks using DropConnect, [in:] Proceedings of the 30th International Conference on Machine Learning, PMLR, vol. 28(3), pp. 1058–1066, Atlanta, Georgia, USA, 2013.

38. S. Brlek, G. Labelle, A. Lacasse, The discrete Green Theorem and some applications in discrete geometry, Theoretical Computer Science, 346(2–3): 200–225, 2005, doi: 10.1016/j.tcs.2005.08.019.
Jul 8, 2021
How to Cite
PATRA, Siddhartha. Designing a Cross Trainer Using an Artificial Neural Network. Computer Assisted Methods in Engineering and Science, [S.l.], v. 28, n. 2, p. 119–138, july 2021. ISSN 2299-3649. Available at: <>. Date accessed: 28 june 2022. doi: