Schedule · Kinematics and Dynamics of Robots

Week	Date	Session	Unit	Topic	Lecture Notes	Reading	Additional Resources
1	Dec 7–13, 2026	C01	I	Robots as Mechanisms	—	SBN 1.7–1.8 SBN 2.1–2.3	RA: Robot motion and freedom (FDP 1–3) Saha: Introductory robot mechanics
		C02	I	Matrix Representation of a point and vector in space	—	SBN 2.4	Saha: Mathematical Fundamentals Spong: Linear Algebra appendix
		C03	I	Representation of a frame at the origin	—	SBN 2.4	RA: Representing orientation (FDP 4) Spong: Rigid Motions and Homogeneous Transformations
2	Dec 14–20, 2026	C04	I	Representation of a frame relative to a fixed reference frame, Representation of a rigid body (Pose)	—	SBN 2.4	Saha: Transformations RA: Local and global frames (FDP 9)
		C05	I	Homogeneous Transformation Matrices (HTM)	—	SBN 2.4–2.5	Modern Robotics: Homogeneous transformations
		C06	I	Representation of pure translation	—	SBN 2.6	RA: Translation demonstration (FDP 5) Saha: Transformations
3	Dec 21–27, 2026	C07	I	Representation of pure rotations	—	SBN 2.6	RA: Rotations about coordinate axes (FDP 6–7)
		C08	I	Representation of combined transformations	—	SBN 2.6	RA: Order and reference frames (FDP 8–9) Spong: Rigid Motions and Homogeneous Transformations
		C09	I	Inverse of transformation matrices	—	SBN 2.5–2.7	Modern Robotics: Homogeneous transformations Saha: Transformations
4	Dec 28, 2026–Jan 3, 2027	C10	II	Introduction to Forward Kinematics, Forward Kinematic Equations for Position	—	SBN 2.8–2.9	RA: FK concepts (FDP 14) RA: Two-link FK (Planar 2)
		C11	II	Forward Kinematic Equations for Orientation	—	SBN 2.10–2.11	Spong: Forward and Inverse Kinematics RA: Three-link FK (Planar 4)
		C12	II	Link and Joint descriptions, D-H parameter table (a, α, d, θ)	—	SBN 2.12	RA: D-H geometry (FDP 10–11) Saha: Kinematics
5	Jan 4–10, 2027	C13	II	Assigning coordinate frames	—	SBN 2.12	RA: Spatial frame assignment (FDP 12) Spong: Forward and Inverse Kinematics
		C14	II	Denavit-Hartenberg (D-H) Representation	—	SBN 2.12	Spong: Forward and Inverse Kinematics RA: D-H visualization (Tutorial)
		C15	II	Deriving the Forward Kinematic equations for common robots (Articulated)	—	SBN 2.11–2.12	RA: Articulated-chain model (FDP 12–13) Saha: Kinematics
6	Jan 11–17, 2027	C16	II	Deriving the Forward Kinematic equations for common robots (SCARA)	—	SBN 2.12	Spong: Forward and Inverse Kinematics, SCARA example RA: FK demonstration (Tutorial)
		C17	II	Deriving the Forward Kinematic equations for common robots (Cylindrical)	—	SBN 2.9 SBN 2.12	Spong: Forward and Inverse Kinematics, cylindrical example Saha: Kinematics
		C18	II	Deriving the Forward Kinematic equations for common robots: Practice problems	—	SBN 2.11–2.12	RA: FK demonstration (Tutorial) Spong: Forward and Inverse Kinematics
7	Jan 18–24, 2027	C19	III	The Inverse Kinematic Solution of Robots, Workspace analysis	—	SBN 1.12 SBN 2.8 SBN 2.13	Modern Robotics: Task space and workspace Saha: Kinematics
		C20	III	Analytical Solutions: Algebraic approach	—	SBN 2.9 SBN 2.13	RA: Two-link inverse solution (Planar 6) Spong: Forward and Inverse Kinematics
		C21	III	Analytical Solutions: Geometric approach	—	SBN 2.9 SBN 2.13	RA: Two-link inverse solution (Planar 6) Saha: Kinematics
8	Jan 25–31, 2027	C22	III	The Inverse Kinematic Solution of Robots: 3-DOF planar arm	—	SBN 2.9–2.11 SBN 2.13	RA: Three-link inverse solution (Planar 8) Spong: Forward and Inverse Kinematics
		C23	III	The Inverse Kinematic Solution of Robots: 3-DOF spatial arm	—	SBN 2.13	RA: Planar and wrist-partitioned IK (FDP 17) Spong: Forward and Inverse Kinematics
		C24	Review	Review for Sessional Examination I	—	SBN 2.4–2.13	Saha: Transformations and Kinematics RA: Three-link inverse solution (Planar 8)
9	Feb 1–7, 2027	No class	—	Sessional Examination I	—	—	—
10	Feb 8–14, 2027	No class	—	Sessional Examination I (until February 9)	—	—	—
		C25	III	Solvability, Degeneracy and Dexterity	—	SBN 2.13 SBN 2.16	Spong: Forward and Inverse Kinematics Saha: Kinematics
		C26	III	The Inverse Kinematic Solution of Robots: 6-DOF arm, wrist center	—	SBN 2.13	RA: Wrist-partitioned IK (FDP 17) Spong: Forward and Inverse Kinematics, kinematic decoupling
		C27	III	The Inverse Kinematic Solution of Robots: 6-DOF arm, inverse orientation	—	SBN 2.10–2.11 SBN 2.13	Spong: Forward and Inverse Kinematics, inverse orientation RA: IK demonstration (Tutorial)
11	Feb 15–21, 2027	C28	III	Inverse Kinematic programming of robots	—	SBN 2.14	RA: Three-link IK program (Planar 9) Saha: Kinematics and Use of Software
		C29	III	The fundamental problem with D-H representation in Inverse Kinematics	—	SBN 2.13 SBN 2.17	Spong: Forward and Inverse Kinematics Saha: Kinematics
		C30	IV	Introduction to Differential Relationships, The Jacobian Matrix	—	SBN 5.1–5.4	Modern Robotics: Velocity kinematics Spong: Velocity Kinematics—The Jacobian
12	Feb 22–28, 2027	C31	IV	Differential motions of a frame versus a robot	—	SBN 5.6–5.7	Spong: Velocity Kinematics—The Jacobian Saha: Kinematics
		C32	IV	Interpretation of differential changes	—	SBN 5.8–5.10	Spong: Velocity Kinematics—The Jacobian Saha: Kinematics
		C33	IV	Calculation of the Jacobian for serial manipulators	—	SBN 5.11	Spong: Velocity Kinematics—The Jacobian Modern Robotics: Velocity kinematics
13	Mar 1–7, 2027	C34	IV	Calculation of the Jacobian for serial manipulators (SCARA or Articulated)	—	SBN 5.10–5.11	Spong: Velocity Kinematics—The Jacobian Saha: Kinematics
		C35	IV	Relationship between the Jacobian and the Differential Operator	—	SBN 5.12	Spong: Velocity Kinematics—The Jacobian Saha: Kinematics
		C36	IV	Singularity Analysis: Decoupling singularities	—	SBN 5.3 SBN 5.5 SBN 5.13 Use Spong for the arm/wrist decoupling treatment.	Spong: Velocity Kinematics—The Jacobian, singularity analysis Modern Robotics: Singularities
14	Mar 8–14, 2027	C37	IV	The Inverse Jacobian	—	SBN 5.13	Spong: Velocity Kinematics—The Jacobian Modern Robotics: Singularities
		C38	V	Lagrangian Mechanics: Short overview of energy-based dynamics	—	SBN 6.1–6.2	Spong: Dynamics Modern Robotics: Lagrangian dynamics, part 1
		C39	V	Kinetic and Potential energy formulations	—	SBN 6.2 SBN 6.4	Spong: Dynamics Modern Robotics: Lagrangian dynamics, part 2
15	Mar 15–21, 2027	C40	V	Effective moments of inertia	—	SBN 6.3	Saha: Dynamics Spong: Dynamics
		C41	V	Dynamic equations for multiple-DOF robots: Two-DOF example	—	SBN 6.2 SBN 6.4	Spong: Dynamics Modern Robotics: Lagrangian dynamics, part 2
		C42	V	Dynamic equations for multiple-DOF robots	—	SBN 6.4	Modern Robotics: Interpreting the mass matrix RA: Inverse dynamics demonstration (Tutorial)
16	Mar 22–28, 2027	C43	V	Static force analysis of robots, Relationship between joint torques and end-effector forces	—	SBN 6.5	Modern Robotics: Serial-chain statics Saha: Statics and Manipulator Design
		C44	V	Transformation of forces and moments between coordinate frames	—	SBN 6.6	Modern Robotics: Combined force and moment representation Saha: Statics and Manipulator Design
		C45	V	Static force analysis of robots: Combined problem and course review	—	SBN 6.4–6.6	Modern Robotics: Serial-chain statics Spong: Dynamics
17	Mar 29–Apr 3, 2027	Buffer	Review	Review/Buffer week	—	—	—

Key

Saeed B. Niku: Introduction to Robotics: Analysis, Control, Applications, 3rd edition (Indian edition), Wiley.
S. K. Saha: Introduction to Robotics, McGraw-Hill Education.
M. W. Spong, S. Hutchinson and M. Vidyasagar: Robot Modeling and Control, Wiley.
RoboAnalyzer: RoboAnalyzer Video Lectures.
Modern Robotics: Videos from Northwestern University.