Basics 3 min read
Lagrangian Formulation of Robot Dynamics
Lagrangian Dynamics In the Newton-Euler formulation, the equations of motion are derived from Newton’s Second Law, which relates force and…
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Physical Interpretation of the Dynamic Equations
In this section, we interpret the physical meaning of each term involved in the closed form dynamic equations for the…
Basics 6 min read
Duality of Differential Kinematics and Statics
We have found that the equivalent joint torques are related to the endpoint force by the Jacobian matrix, which is…
Basics 8 min read
Inverse Kinematics of Differential Motion
Now that we know the basic properties of the Jacobian, we are ready to formulate the inverse kinematics problem for…
Basics 3 min read
Properties of the Jacobian
The Jacobian plays an important role in the analysis, design, and control of robotic systems. It will be used repeatedly…
Basics 2 min read
Differential Motion
In the previous chapter, the position and orientation of the manipulator end-effecter were evaluated in relation to joint displacements. The…
Basics 2 min read
Kinematics of Parallel Link Mechanisms
Consider the five-bar-link planar robot arm Note that Joint 2 is a passive joint. Hence, angle θ2 is a dependent…
Basics 4 min read
Inverse Kinematics of Planar Mechanisms
The vector kinematic equation derived in the previous section provides the functional relationship between the joint displacements and the resultant…
Basics 5 min read
Planar Kinematics
Kinematics is Geometry of Motion. It is one of the most fundamental disciplines in robotics, providing tools for describing the…
Basics 2 min read
Parallel Linkages
Primitive joints can be arranged in parallel as well as in series. Figure 3.2.1 illustrates such a parallel link mechanism.…