This thesis is motivated by practical problems encountered in handling live products in the poultry processing industry, where live birds are manually transferred by human labors. As the task of handling live products is often unpleasant and hazardous, it is an ideal candidate for automation. To reduce the number of configurations and live birds to be tested, this thesis focuses on developing analytical models based on the Lagrange method to predict the effect of mechanical inversion on the shackled bird. Unlike prior research which focused on the effect of different inversion paths on the joint force/torque of a free-falling shackled bird, this thesis research examines the effect of kinematic constraints (designed to support the bird body) on the shackled bird. Unlike free-falling, the imposed kinematic constraints enable the shackled bird to rotate about its center of mass, and thus minimize wing flapping. In this thesis, birds are geometrically approximated as ellipsoids while the lower extremity is modeled as a pair of multi-joint serial manipulators. With the constraint equations formulated into a set of differential algebraic equations, the equations of motion as well as Lagrange multipliers characterizing kinematical constraints are numerically solved for the bird motion, specifically the position, velocity, and orientation and hence the forces and torques of the joints. The dynamic models are verified by comparing simulation results against those obtained using a finite element method. The outcomes of this thesis will provide some intuitive insights essential to design optimization of a live-bird transfer system.