We study different parametrizations of the angular space of polyatomic molecules for an orthogonal description of the molecular geometry. Kinetic energy operators for pentatomic molecules, given by compact and computationally useful forms in a global and a local formulation of the axis system, are compared and discussed. A new decomposition of T for sequentially bonded pentatomic molecules in conjunction with a basis of Wigner and associated Legendre functions provides kinetic energy matrix elements which are free of singularities. Practical problems caused by an unusual volume element for a description involving only intervector (bending) angles are addressed. The corresponding rovibrational kinetic energy operators are derived for the two-vector body-fixed formulation.