In the P$-$P$-$P robotic manipulator, the linear displacement variables ${}_{1y^{\text{'}}}{}_{2y\text{'}}$ and ${}_{3z}$ are not

often assigned constant values because they correspond to the translational displacements

of the prismatic joints. More often, displacement ranges are assigned to these variables.

Example $11\mathrm{.}3$

Problem Statement: Using the joint displacements given in Table E$\mathrm{.}11\mathrm{.}2,$ calculate the

global path points achieved by the end effector of the P$-$P$-$P robotic manipulator. In this

example, ${?}^3\{p_3\}=[0,-1,0{]}^T.$

Known Information: Equation $11\mathrm{.}12$ and Table E$\mathrm{.}11\mathrm{.}2.$

Solution Approach: Table E$\mathrm{.}11\mathrm{.}3$ includes the global end effector path point coordinates

calculated using Equation $11\mathrm{.}12.$

TABLE E$\mathrm{.}11\mathrm{.}2$

P$-$P$-$P Robotic Manipulator Joint Displacements

TABLE E$\mathrm{.}11\mathrm{.}3$

P$-$P$-$P Robotic Manipulator Path Point Coordinates