Skip to main content
SpringerLink
Log in

Software modeling of multi-degree-of-freedom motion system using matrices

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

This paper presents the results of the research of multi-degree-of-freedom robot motion with multiple degrees of freedom by using a mechanical model of transformation of the matrix that can be used in solving the kinematics of the robots whose internal structure of the joints allows only the rotation. The matrices of rotation transformations and their application in different cases of robot motion, such as the first step, the second, third, and fourth steps, are set out. The research which was conducted in this work is a part of the development of mechatronic systems, and the results obtained by this method are suitable to solve problems of the anthropomorphic of robots and can be used for other purposes in various areas of mechanical engineering. Mechanism with multiple degrees of freedom, such as a mechanical robot system, occupies a number of positions necessary to carry out the task. Thus the position of the mechanical system is determined by a set of internal coordinates that determine the movement of the joints. It is understood that the movement is a requirement that each of the coordinates governed by its law determines the position of the robot movement, through the so-called internal and external coordinates. It also determines the way of conversion of coordinates from one movement to another, or the application of equations to solve the kinematics problems of robots (robots determine the vector segments, segment positioning, angle and line speed, angle and line acceleration). The movement of the joints is achieved with the use of an motor, which allows only rotation movement. By applying the static equilibrium of the centrer of gravity of the robots, a part of the research of an anthropomorphic robot with 18 degrees of freedom, allowing the development of a mechatronic system, whose results allow the movement of the robot position in stages, is carried out. The largest part of the investigation described in the paper was performed on a computer, applying powerful software.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

\({\varvec{r}}\) :

Position vector

\({\varvec{r}}_{i}\) :

Position vector \(i\)-th segment

\({\varvec{r}}_{D}\) :

Vector points D

\({\varvec{r}}_{D}^{\left( 0 \right)}\) :

Position vector of point \(D\) the immobile coordinate system

\({\varvec{r}}_{{S_{i} }}\) :

Joint position vector \(S_{i}\) \(i\)-th segment

\({\varvec{r}}_{{S_{i} }}^{\left( 0 \right)}\) :

Initial joint position vector \(S_{i}\) the immobile coordinate system

\({\varvec{r}}_{{S_{n} }}^{\left( 0 \right)}\) :

Vector sum of the joint segments \(S_{n}\)

\({\varvec{r}}_{{C_{i} }}\) :

Gravity vector segments

\({\varvec{r}}_{{C_{i} }}^{\left( 0 \right)}\) :

Centre of gravity position vector segments \(C_{i}\) the immobile coordinate system

\({\varvec{l}}\) :

Vector segments

\({\varvec{l}}_{i}\) :

Vector of i-th segment

\({\varvec{l}}_{2}^{\left( 1 \right)} = {}^{1}{\varvec{R}}_{2} {\kern 1pt} {\varvec{l}}_{2}^{\left( 2 \right)}\) :

The transformation of vectors from the other coordinate system in the firs coordinate system

\({}^{0}{\varvec{R}}_{i}\) :

Rotational transformation matrix of a moving-coordinate system i-that in relation to the immobile

References

  1. Ambe Y, Matsuno F (2016) “Leg–grope walk”: strategy for walking on fragile irregular slopes as a quadruped robot by force distribution. Robomech J 3(7):1–17

    Google Scholar 

  2. Bottega V, Pergher R, Fonseca JSO (2009) Simultaneous control and piezoelectric insert optimization for manipulators with flexible link. J Braz Soc Mech Sci Eng. 31(2):105–116

    Article  Google Scholar 

  3. Cho J, Kim JT, Kim J, Park S, Kim K II (2016) Simple walking strategies for hydraulically driven quadruped robot over uneven terrain. J Electr Eng Technol 11(5):1433–1440

    Article  Google Scholar 

  4. Duffert U (2004) Gait on four legs-modeling and optimization of robot motion. Dissertation, Humboldt-University Berlin

  5. Fu KS, Gonzalez RC, Lee CSG (1989) Robotics: control, sensing, vision and intelligence. Mc Graw-Hill Book Company, New York

    Google Scholar 

  6. Golubovic D, Hu H (2002) An interactive software environment for gait generation and control design of Sony legged robots. In: Proceedings of the 5th international symposium on robo cup, Fukuoka, Japan, pp 279–287

  7. Golubovic D, Hu H (2002) A Hybrid evolutionary algorithm for gait generation of sony legged robots. In: The 28th annual conference of the IEEE industrial electronics society, Sevilla, Spain

  8. Guardabrazo TA, Jimenez MA, Gonzalez de Santos P (2006) Analysing and solving body misplacement problems in walking robots with round rigid feet. Robot Auton Syst 54(3):256–264

    Article  Google Scholar 

  9. Jahanbin Z, Selk Ghafari A, Ebrahimi A, Meghdari A (2016) Multi-body simulation of a flapping-wing robot using an efficient dynamical model. J Braz Soc Mech Sci Eng 38(1):133–149. doi:10.1007/s40430-015-0350-4

    Article  Google Scholar 

  10. Kuznetsov YA, Goncharenko VV, Kalashnikova LV, Strebkov SV, Slobodyuk AP, Bondarev AV (2016) Repair of engine radiator by means of cold gas spraying. Appl Eng Lett 1(2):57–60

    Google Scholar 

  11. Lewis MA, Bekey GA (2002) Gait adaptation in a quadruped robot. Auton Robots 12(3):301–312

    Article  MATH  Google Scholar 

  12. Li T, Liu X, Xie F (2013) Type synthesis of 4-DOF parallel kinematic mechanisms based on Grassmann line geometry and atlas method. Chin J Mech Eng 26(6):1073–1081

    Article  Google Scholar 

  13. Mikic D (2005) Mechanical modeling of anthropomorphic robot using the matrix transformation. Master Thesis, University of Kragujevac, Faculty of Engineering Cacak, Serbia

  14. Sony Corporation (2004) Installation guide for ERS-210: OPEN-R SDK documents English. http://www.tekkotsu.org/openr-install.html. Accessed 24 Jan 2012

  15. Sony Corporation (2002) Model information for ERS-210: OPEN-R SDK documents English. http://www.informatik.uni-bremen.de/~roefer/kr02/ModelInforation_210_E.pdf. Accessed 6 Feb 2012

  16. Spasic D, Meza S, Adamović Ž (2016) Implementation computer systems for maintenance management (computerized maintenance management system-CMMS). Tech Diagn 15(2):40–46

    Google Scholar 

  17. Stefanovic S, Mikic D, Golubovic D, Ilic D (2013) Modeling and simulation of robot KR80 series based on Matlab software program. Ann Fac Eng Hunedoara 11(3):161–168

    Google Scholar 

  18. Sun Q, Wang C, Zhao D, Zhang C (2014) Cam drive step mechanism of a quadruped robot, Hindawi Publishing Corporation. J Robot 2014:1–9

    Google Scholar 

  19. Vukobratovic M, Borovac B, Surla D, Stokic D (1990) Biped locomotion—dynamics, stability and application. Springer, Berlin

    Book  MATH  Google Scholar 

  20. Wang H, Qi Z, Xu G, Xi F, Hu G, Huang Z (2010) Kinematics analysis and motion simulation of a quadruped walking robot with parallel leg mechanism. Open Mech Eng J 4(1):77–85

    Article  Google Scholar 

  21. Wang H, Sang L, Hu X, Zhang D, Yu H (2013) Kinematics and dynamics analysis of a quadruped walking robot with parallel leg mechanism. Chin J Mech Eng 26(5):881–891

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technical School, Gornji Milanovac, Serbia

    Danilo Mikić

  2. University of Novi Sad, Technical Faculty ,,Mihajlo Pupin”, Zrenjanin, Serbia

    Eleonora Desnica

  3. Technical College, Kragujevac, Serbia

    Nikola Radivojević

  4. University Business Academy, Faculty of Economics and Engineering Management, Novi Sad, Serbia

    Aleksandar Ašonja

  5. Metropolitan University, Belgrade, Serbia

    Vladimir Milićević

Authors
  1. Danilo Mikić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eleonora Desnica
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nikola Radivojević
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Aleksandar Ašonja
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Vladimir Milićević
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikola Radivojević.

Additional information

Technical Editor: Sadek C. Absi Alfaro.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mikić, D., Desnica, E., Radivojević, N. et al. Software modeling of multi-degree-of-freedom motion system using matrices. J Braz. Soc. Mech. Sci. Eng. 39, 3621–3633 (2017). https://doi.org/10.1007/s40430-017-0745-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40430-017-0745-5

Keywords

Search

Navigation