Robot Kinematics EFPAC FINAL PROJECT KINEMATICS Overview Robot

Robot Kinematics

EFPAC FINAL PROJECT- KINEMATICS Overview Robot kinematics describes the pose, velocity, acceleration, and all higher-order derivatives of the pose of the bodies that comprise a mechanism.

EFPAC FINAL PROJECT- KINEMATICS Position and Orientation Representation of the spatial pose of a body in order to control the robot displacement and rotation.

EFPAC FINAL PROJECT- KINEMATICS Position and Displacement Using a vector we can move from the origin of the coordinate frame i to the coordinate frame j.

EFPAC FINAL PROJECT- KINEMATICS Orientation and Rotation Using the basis vectors (Xi, Yi, Zi) we can rotate and orientate the coordinate frame to any other position using the rotation matrix.

EFPAC FINAL PROJECT- KINEMATICS Orientation and Rotation The velocity relationship is calculated by using Euler angles method, in order to define the successive rotation of the angles.

EFPAC FINAL PROJECT- KINEMATICS Homogeneous Transformations To combine together the position vectors and orientation matrices in a compact equation.

EFPAC FINAL PROJECT- KINEMATICS Joint Kinematics The surfaces of two bodies that are in contact to each other and transmit the motion from one to another. Are classified as: • Lower pair joints. • Higher pair joints. • 6 -DOF joint.

EFPAC FINAL PROJECT- KINEMATICS Workspace The volume of a robotic manipulator is the maximum area that the end-effector can reach.

EFPAC FINAL PROJECT- KINEMATICS Geometric Representation Using reference frames we could define the links of a robotic manipulator, under the Denavit and Hartenberg methods.

EFPAC FINAL PROJECT- KINEMATICS Forward Kinematics Knowing the joints position and the values of the geometric link parameters determine the position and orientation of the end-effector relative to the base. Inverse Kinematics Knowing the position and orientation of the end-effector and the values of the geometric link parameters determine joints position.

EFPAC FINAL PROJECT- KINEMATICS Forward Instantaneous Kinematics With position and the rates of motion of the joints we can calculate the end-effector´s total velocity. Inverse Instantaneous Kinematics With position and the end-effector´s total velocity we can calculate the rates of motion of the joints.

EFPAC FINAL PROJECT- KINEMATICS Static Wrench Transmission The wrenches that is applied, is the endeffector relationship with the forces/torques of the joints.

EFPAC FINAL PROJECT- KINEMATICS Conclusions • Representations of the position and orientation. • Freedom of motion of the joints. • Geometric representation and the workspace. • Forward and inverse (instantaneous) kinematics. • Transmission of static wrenches.

Thank you! 18 Jul 2016