Movement is one of the essential characteristics of living beings. Despite the diversity of animal species and the apparent differences, standard features exist between their movement systems that follow a particular pattern. The movements can mainly be divided into discrete and rhythmic categories controlled by the central nervous system. Scientists usually consider these two types of motion separately in the control system and use different methods and resources to produce and model them. Proposing a unified and comprehensive model for generating and controlling rhythmic and discrete movement with the same control system is more valuable, albeit challenging. This is essential because such a model would address a fundamental problem in the field of motor control, offering a holistic solution to understanding how living beings generate and control movement. A unified model could revolutionize various fields, including robotics, rehabilitation, and neuroscience, by providing a versatile framework applicable to various applications. In this study, we employed the Hodgkin-Huxley (HH) equations in our computational model; their suitability lies in their ability to capture the intricate dynamics of neural oscillations and the behavior of neural networks, making them an ideal choice for our investigation. Our comprehensive analysis of the model, factors influencing motion, and oscillation revealed crucial insights. We found that supraspinal input and motor neuron feedback, as the key motor control parameters, play pivotal roles in generating and controlling rhythmic and discrete movements. These findings contribute to our understanding of how the nervous system orchestrates both types of motion within a single framework. Developing a neuromechanical model capable of creating rhythmic and discrete movements holds promising implications. This research can potentially advance fields such as robotics, biomechanics, and rehabilitation by providing a unified framework for motor control. Moreover, understanding the switching mechanism between rhythmic and discrete states could lead to innovative strategies for designing more versatile and adaptive robotic systems and improving rehabilitation protocols for individuals with motor impairments.