Knowledge prerequisites

From WikIRI

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Here's a list of concepts you'd better review, before enrolling in the course Kinematic Geometry of Robot Mechanisms

Concepts needed from Linear Algebra

• Definition of vector space
• Basis of a vector space
• Dimension of a vector space
• Linear dependence of vectors
• Linear application
• Matrix representation of a linear application
• Rank of a matrix
• Spaces associated to a linear application: the kernel and range spaces
• Determinant of a matrix and how to compute it
• Inverse of a matrix
• Relationship between the dimensions of the kernel and the range spaces
• Orthogonality (dot product, cross product, orthogonal complements)
• Rotation matrices

A good book where these concepts can be reviewed is Introduction to linear algebra by Prof. Gilbert Strang from MIT, and in the associated video lectures. The book can be found in English and Spanish in the library of the UPC.

Concepts from mechanics

From statics:

• Concepts of force and torque
• Moment of a force with respect to a point
• Resultant of a system of forces and torques
• Free-body diagrams
• Concept of rigid body
• Conditions for equilibrium on a rigid-body.
• Basic knowledge on computing unknown forces on statically determinate mechanical systems.
• Power generated by a force and by a torque

From Kinematics:

• Concepts of linear and angular velocity
• Instant center in planar kinematics
• Instantaneous screw axis in spatial kinematics
• Composition of velocities in different reference frames

A good book where these concepts can be reviewed is Vector Mechanics for Engineers by Ferdinand P. Beer and E. Russell Johnston. The book can be found in English and Spanish in the library of the UPC.

Programming

Besides the previous concepts, the student should have working knowledge of some computer language, as some of the course exercises require a bit of programming. For that purpose, experience in Matlab, GNU-Octave, or C will suffice.

For those using Matlab, this cheat sheet from MIT might be useful.