Jacob Ward Portfolio
6-Bar Linkages
Project 1 for Robotics Mechanics & Control focused on analyzing the mobility, forward kinematics, and singularities of two different 6-bar linkages: the Stephenson III and Klann linkages. A CAD model was made for each linkage to 3D print a scale model to supplement the analysis.
Stephenson III
The Stephenson III six-bar linkage consists of six interconnected links with revolute joints to generate quasi-straight-line motion using only rotary actuators. Using Grübler’s equation, the linkage was determined to have one degree of freedom (DOF), meaning its configuration is fully defined by the crank angle θ. To analyze its motion, the CAD model shown was created followed by a 3D-printed prototype. Motion simulations in SolidWorks were conducted to trace the output motion of the end-effector, and a singularity analysis identified conditions where driving the mechanism with improper links could cause it to lock and invert into an unintended configuration.
Klann Linkage
The Klann six-bar linkage consists of six interconnected links with revolute joints, designed to replicate legged locomotion by converting rotary motion into a walking gait. Using Grübler’s equation, the linkage was determined to have one degree of freedom (DOF), meaning its configuration is fully defined by the crank angle α. To analyze its motion, the CAD model shown was created, followed by a 3D-printed prototype. Motion simulations in SolidWorks were conducted to trace the path of the leg end-effector, revealing a characteristic lift and propulsion phase that enables efficient ground traversal. A singularity analysis identified conditions where driving the mechanism with improper links could cause it to lock and invert, disrupting its intended motion.
3R Robot Falling
Project 2 explored the dynamics of a planar 3R robot arm falling under gravity, using Lagrangian mechanics to derive its equations of motion. The system consists of three revolute joints with concentrated masses at each link tip, and its motion is governed by the Euler-Lagrange equations. The kinetic and potential energy of the arm were formulated to compute the system’s mass matrix, Coriolis/centripetal forces, and gravitational torques, allowing for a precise simulation of its behavior. Using MATLAB, an Euler integration approach was implemented to iteratively update joint angles and velocities over time. The simulation traced the end-effector trajectory, showing how the arm collapses dynamically from an initial outstretched position. Finally, an animated visualization was generated to illustrate the arm’s motion, providing insights into the effects of gravity on robotic systems and potential extensions such as friction modeling and real-world validation.
