A study of the inverse kinematics for a five-degree-of-freedom (DOF) spatial parallel micromanipulator is presented here below. The objective of this paper is the introduction of a structural and geometrical model of a novel five-degree-of-freedom spatial parallel micromanipulator, analysis of the effective and useful workspace of the micromechanism, presentation of the obtained analytical solutions of the microrobot’s inverse kinematics tasks, and verification of its correctness using selected computer programs and computation environments. The mathematical model presented in this paper describes the behaviour of individual elements for the applied 2-DOF novel piezoelectric actuator, resulting from the position and orientation of the microrobot’s moving platform. 1. Introduction Over the past years much attention has been devoted to the analysis of parallel micromanipulators [1, 2]. These mechanisms have a major advantage over serial microrobots, reflected inter alia in their accuracy, repeatability, and speed, with which the desired position can be achieved [3–5]. On the other hand, the parallel manipulators have a relatively smaller workspace, limited by the maximum arms lengths, angle values at the joints, and their dimensions. Moreover, the main difficulty with parallel manipulators (both in micro- and macroscale) is the complexity of controlling their movement. Kinematic structures of various types of parallel mechanisms may contain serial, parallel, or serial-parallel (hybrid) types of linkages, mounted to the platforms by universal joints [6–10]. The desired position and orientation of the moving platform are achieved by combining the linear and angular lengths of the robot’s arms, transformed by their degrees of freedom into three positional and orientational ones for the operating member [11–13]. The problem of inverse kinematics task for spatial parallel manipulators can be defined as finding the linkage’s lengths needed to position the moving platform along a specified geometric path, aligned accordingly with the desired orientation [14–17]. The solution to this problem can sometimes be indeed very complex and less suitable for real-time computing. However, the computation of length for each arm can be carried out independently, which can additionally speed up the process [18]. This procedure is used to guide the moving platform in controlling its movement [16, 19]. Quoted features constitute the greatest importance when it comes to designing and constructing parallel platforms, operating in micro- or nanometric scales [20–23]. Thus far,
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