Characterization of The Fourth-Order S-curve Trajectory Using Unitization Method


  • Rupesh Tatte, Hemant Jawale, Hemant Thorat


Critical motion parameter, Multiplication factor, Velocity, Unitized value


In point-to-point motion transfer applications such as CNC machines, where the tool is required to move along a pre-planned path with high speed and precision, vibration is a common issue that can lead to degradation of positional accuracy. This issue is addressed with the help of trajectory planning, where the implementation of an S-curve trajectory is reported to result in high positional accuracy compared to a trapezoidal velocity trajectory. This paper introduces the different properties of fourth-order symmetrical S-curve trajectory for the point-to-point motion transfer system. Complex mathematics is required to acquire the desired values of motion parameters of the trajectory. Therefore, the paper proposes a novel unitization approach that treats time and displacement as one unit each and simplifies the complex mathematics. This method provides a single generalized solution for any displacement and motion time value. The paper illustrates graphical relationships among motion parameters such as peak values of velocity, acceleration, jerk, and snap, which can serve as nomograms for choosing appropriate values to design displacement trajectories. Using these graphs, the paper outlines simple guidelines for selecting suitable values of motion parameters adapted to common situations. Finally, a case study is presented to validate feasibility of the proposed method.


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How to Cite

Hemant Jawale, Hemant Thorat, R. T. . (2024). Characterization of The Fourth-Order S-curve Trajectory Using Unitization Method. International Journal of Intelligent Systems and Applications in Engineering, 12(3), 2141–2149. Retrieved from



Research Article