Kinematic Modeling of a Walking Robot Lower Limb with Upper Actuator Placement

This paper presents the development of a kinematic model for the lower limb of a quadruped walking robot. The key feature of the model is the placement of all actuators within the hip joint housing, where torque from the drive shaft is transmitted to the shin via a lever mechanism. The advantage of this design is the reduced mass of the lower limb, which enhances the limb’s response speed to control signals and increases the overall maneuverability of the robot. The disadvantage is the increased kinematic complexity, which necessitates deriving the relationships between the angular displacements of the components. The aim of this work is to develop a complete kinematic model of the lower limb of a quadruped robot, with the actuators for both the thigh and shin segments located within a single hip joint unit, where torque from the drive shaft is transmitted to the shin through a lever mechanism. This approach reduces the mass of the lower limbs and overcomes the drawbacks inherent to classical kinematic configurations. In this study, the relationship between the actuator shaft rotation angle and the resulting shin deflection relative to the thigh was derived. To validate the model, equations describing the ankle point trajectory during the walking process were formulated. Using the obtained coordinates, the angular variations were calculated by solving the inverse kinematics problem. The resulting graphs of these angular changes are smooth and continuous, which is a necessary condition for ensuring impact-free motion of the lower limb. Verification using a 3D solid model in SolidWorks confirmed the absence of mechanical interference (collisions) between links across all calculated positions. The obtained results constitute a complete mathematical framework for the design and control of energy-efficient limbs for walking robots. Thus, this work lays the foundation for creating lighter and more dynamic robotic platforms applicable in inspection, monitoring, and autonomous navigation tasks in complex environments.

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