Chapter 3 – Kinematics Definition: (a) The branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion. (b) The features or properties of motion in an object, regarded in such a way. “Kinematics can be used to find the possible range of motion for a given mechanism, or, working in reverse, can be used to design a mechanism that has a desired range of motion. The movement of a crane and the oscillations of a piston in an engine are both simple kinematic systems. The crane is a type of open kinematic chain, while the piston is part of a closed four‐bar linkage.” Distinguished from dynamics, e.g. F = ma Several considerations: 3.2 – 3.2.2 How do wheels motions affect robot motion (HW 2) 3.2.3 Wheel constraints (rolling and sliding) for Fixed standard wheel Steered standard wheel Castor wheel Swedish wheel Spherical wheel 3.2.4 Combine effects of all the wheels to determine the constraints on the robot. “Given a mobile robot with M wheels…” 3.2.5 Two examples drawn from 3.2.4: Differential drive. Yields same result as in 3.2 (HW 2) Omnidrive (3 Swedish wheels) Conclusion (pp. 76‐77): “We can see from the preceding examples that robot motion can be predicted by combining the rolling constraints of individual wheels.” “The sliding constraints can be used to …evaluate the maneuverability and workspace of the robot rather than just its predicted motion.” 3.3 Mobility and (vs.) Maneuverability Mobility: ability to directly move in the environment. “In addition…a mobile robot [or any machine] is able to further manipulate its position OVER TIME, by steering steerable wheels.” Consider moving your bicycle from a starting position to a pose which is exactly parallel but 1 meter to the left. “the overall maneuverability of a robot is thus a combination of the mobility available based on the kinematic sliding constraints of the standard wheels, plus the additional freedom contributed by steering and spinning the steerable standard wheels.” ICR – instantaneous center of rotation Ackerman steering Degree of steerability. 3.4 Workspace: all possible configurations (poses). Velocity space: independent components of velocity the robot can control. Also called DDOF = differential degrees of freedom. Example: Unicycle‐ velocity space has two axes, one for forward speed, one for rotation. Path & trajectory. See example pp. 88‐89 .