what would be the linear equation that defines the xyz coordinate movement and orientations of each appendages/joints(muscle not necessary included) in locomotion gaits of bipedal or any pedal walkers(such as pictured)while also including posture changes given variables like condition, weight and speed?

i suppose the result to expects are posture and silhouette but maybe i ll iterate those myself once the world coordinates or polar/spherical coordinates are solved.... how many ways can i approach this anyway