Kinematic and Dynamic Parameters of a Robotic Mechanism

The second important modelling tool used in this book is the general joint model (tf Roberson and Schwertassek [36]. This model allows arbitrary joints and contacts to be described using orthogonal sets of vectors which are associated with the free and constrained modes of motion of the joint or contact Multiple degree-of-freedom joints are easily included in any analysis. It is a particularly useful tool in the context of closed chains, since contacts which are part of 

Many of the notational conventions presented here are based on concepts introduced by Roberson and Schw ssek in [36] and used by Brandi, Jdtanni, and Otter in [3]. They are similar in many ways to those described by Feather-stone in [9], although there are a few minOT differences. 

For single-axis joints, the matrix functions used to transform vector quantities between coordinate frames are functions of these four parameters. These transformations will be defined in the following pages. The modelling conventions used for more complex joint structures will be discussed in the next section. 

In spatial notation, velocity, acceleration, and force vectors are all 6 x 1 column vectors, and each incorporates the appropriate linear and angular com- 

In general, the transformation of a spatial vector quantity from one coordinate system to an adjacent one may be accomplished by the following spatial multiplication [9]  

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