Forward kinematic problem of two 4-RRUR with different geometric structures and one 4-RUU parallel robots

In this paper, the forward kinematic of the special cases of 4- R" R' R' R" R", 4- R" R" R" R' R' and 4- R" R" R' R' R" parallel mechanisms that respectively lead to two 4- R R U R with different geometric structures and one 4- R U U spatial 4-DOF parallel robots has been studied. They are originated from the type synthesis of 4-DOF parallel mechanisms with motion patterns of 3 T1R. Each of them is composed of four kinematic chains and each chain consists of five revolute joints. The directions of revolute joints have been different with each others that create three different geometrical structures. The forward kinematic problem is done in three dimensional Euclidean space and finally, a univariate mathematical expression of degree 344, 462 and 8 is indicated the forward kinematic problem of each parallel robot. Also, the results are compared with simulations.