OICC Press International Journal of Mathematical Modelling & Computations 2228-6233 16 3 2026 09 30 Designing a Cat Robot with a Defective Leg Capable of Jumping Stairs 190 206 10.57647/ijm2c.2026.1603.15 EN Mehrdad NaghshNilchi Department of Mechanical Engineering, Na.C., Islamic Azad University, Najafabad, Iran https://orcid.org/0009-0005-2259-0771 Mohammad Saadat Department of Mechanical Engineering, Na.C., Islamic Azad University, Najafabad, Iran https://orcid.org/0009-0006-5702-5817 Ali Soleimani Department of Mechanical Engineering, Na.C., Islamic Azad University, Najafabad, Iran https://orcid.org/0000-0003-2189-6443 Meisam Vahabi Department of Mechanical Engineering, Na.C., Islamic Azad University, Najafabad, Iran Mehdi Salehi Department of Mechanical Engineering, Na.C., Islamic Azad University, Najafabad, Iran https://orcid.org/0000-0002-7090-7973 Journal Article 2026 09 30 Many scientists utilize the movement behavior of animals in nature to design and simulate robots. Jumping over obstacles is one of the most crucial and challenging tasks for four-legged robots. However, errors can occur when these robots attempt to jump on stairs. If one leg of the four-legged robot is defective, appropriate adjustments can be made to enable the robot to still jump on stairs. This paper focuses on simulating the jumping motion of a four-legged robot, which is considered one of the most challenging aspects of controlling such robots. Initially, a two-dimensional model of the four-legged robot is introduced, followed by the formulation of dynamic equations that govern the robot's jumping motion. This operation is subsequently simulated using Adams software, whereby the robot's jump is modeled through torsion springs in each leg. One of the most challenging scenarios discussed in this article involves the four-legged robot jumping on stairs with a defective leg. The robot's jump on the stairs is then optimized based on various parameters, and the best case scenario of the robot jumping on stairs with a defective leg is presented. This optimized case is illustrated in diagram form within the article.