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When a machine tool is mounted at the tip of a robotic manipulator, the manipulator becomes more flexible (the natural frequencies are lowered). Moreover, for a given flexible manipulator, its compliance will be different depending on feedback gains, configurations, and direction of interest. Here, the compliance of a manipulator is derived analytically, and its magnitude is represented as a compliance ellipsoid. Then, using a two-link flexible manipulator with an abrasive cut off saw, the experimental investigation shows that the chattering varies with the saw cutting angle due to different compliance. The main work is devoted to finding a desirable cutting angle which reduces the chattering.

Initial experiments on state-space feedback control of a large flexible manipulator with a parallel linkage drive are described. A linear controller using joint angle and strain measurements has been designed to minimize a quadratic performance index with a prescribed stability margin. It is based on a simplified model that accounts for the constraints of the parallel linkage kinematically rather than through constraint forces. The results show substantial improvement over a simple proportional-derivative joint control.

The potential benefits of the ability to control more flexible mechanical arms are discussed. A justification is made in terms of speed of movement. A new controller design procedure is then developed to provide this capability. It uses both a frequency domain representation and a state variable representation of the arm model. The frequency domain model is used to update the modal state variable model to insure decoupled states. The technique is applied to a simple example with encouraging results.

The modeling via transfer matrices of mixed lumped-distributed parameter systems with feedback control is discussed and novel methods of obtaining information on the controlled system's dynamic response via numerical methods is presented. These methods utilize numerical searches in the complex plane for the roots of the transcendental characteristic equation to determine the closed loop system eigenvalues. The fast Fourier transform (FFT) algorithm is utilized but in the inverse fashion (from frequency domain to time domain). The information obtained is identical to that contained in a model in modal coordinates, and can be used to construct such a model. An interactive computer program to do the required calculation is described, as well as its application to a manipulator arm design problem.

The control of the flexible motion in a plane of two pinned beams is addressed with application to remote manipulators. Three types of linear feedback control schemes are considered: joint angle and velocity feedback with (GRC) and without (IJC) cross joint feedback, and feedback of flexible state variables (FFC). Two models of the distributed flexibility are presented along with some results obtained from them. The relative merit of the three control schemes is discussed.

The study of various aspects of manipulator design and control is summarized, focusing on the interaction of the structure's flexible dynamics and the dynamics of the joint control system, including specific information on modeling and design, modal analysis and control, and the flexible manipulator analysis computer program, FMAP.

The Flexible Manipulator Analysis Program (FMAP) is a collection of FORTRAN coding to allow easy analysis of the flexible dynamics of mechanical arms. The user specifies the arm configuration and parameters and any or all of several frequency domain analyses to be performed, while the time domain impulse response is obtained by inverse Fourier transformation of the frequency response. A detailed explanation of how to use FMAP is provided.

The interactions of control system and distributed flexible structural dynamics is explored for mechanical arms. A modeling process using 4 x 4 transfer matrices is described which permits the closed loop response of many current arm configurations to be evaluated. Root locus, frequency response, modal shapes, and time impulse response have all been obtained from the digital computer implementation of this model, which is oriented to arm design and allows for easy variation of the arm configuration through data cards. The model corresponds with experimentally observed natural frequencies with an average error of less than 5% in the first three flexible modes in the seven cases considered. The model was used to explore the limits imposed by structural flexibility on a nondimensionalized two link arm with one and two joints for planar motion.

This paper is a progress report summarizing theoretical and practical results concerning integration of design and control aspects of manipulator arms for industrial or space applications. The relationships between task specifications, gross motions, fine motions, actuator type and location, size and strength of structural members, control servos and strategies, and overall design evaluation are briefly discussed, with some technical examples.

An investigation is reported involving a mathematical procedure using 4 x 4 transformation matrices for analyzing the vibrations of flexible manipulators. Previous studies with the procedure are summarized and the method is extended to include flexible joints as well as links, and to account for the effects of various power transmission schemes. A systematic study of the allocation of structural material and the placement of components such as motors and gearboxes was undertaken using the analytical tools developed. As one step in this direction the variables which relate the vibration parameters of the arm to the task and environment of the arm were isolated and nondimensionalized. The 4 x 4 transformation matrices were also used to develop analytical expressions for the terms of the complete 6 x 6 compliance matrix for the case of two flexible links joined by a rotating joint, flexible about its axis of rotation.