This is the second part of the four-part series paper, where the novel mathematical dynamical modelling of transtibial prosthetic leg has been developed, which will be used in the algorithm for guidance and calculating the approximate trajectory of movements with the aim to help amputee’s patients with dementia, paralysis,  monoplegia, hemiplegia, paraplegia, cancer, infection or from induced virus/parasites, which impairs decision making. The hardware of ankle joint motor and metatarsophalaneal joint motor with beta logic been explained. The mathematical 4-rod pendulum equations with Lagrangian and Hamilton are developed for four rigid links and gait cycle. The mathematical models developed in these papers are also useful for doctors in studying gait and finding the solution for ailments, various abnormalities and disorders of the musculoskeletal system. The model has been tested in simulation and found to be promising to be tested for clinical purposes,even the patellar reflex arc test has shown positive response from the leg; this reduces the expenses which even after expenses is ineffective but not been clinically tested.