TAILIEUCHUNG - Parallel Manipulators Towards New Applications Part 2

Tham khảo tài liệu 'parallel manipulators towards new applications part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 28 Parallel Manipulators Towards New Applications Base parameters An important characteristic of the system expressed by equation 20 is that some inertial parameters do not affect the dynamics of the manipulator and others have a relative effect with respect to the other parameters on the external generalized forces. Mathematically this can be expressed by the presence of zero columns in the observation matrix W and the dependence that exist between others. Hence this system never could be considered as a determined one. The minimal number of parameters that are needed to determine uniquely the dynamics of the system has to be calculated. This set of parameters is known as the base parameters and can be considered as a combination with the others that have an effect. The number of base parameters is equal to the rank of the observation matrix. The base parameter combination can be calculated principally in two ways analytically Khalil Bennis 1995 or numerically using the Singular Values Decomposition SVD or QR factorization Gautier 1991 . The analytical analysis will not be considered here since for a parallel manipulator its application is not direct. Analytical calculation of the base parameters have already been presented for close chains mechanical systems Khalil Bennis 1995 however the method is applicable only to some particular topologies. The use of SVD is characterized by its precision while the QR factorization by its low computational cost. The first case is of interest to us since the precision of the resulting inertial parameters identified is more important. As an example consider the 3-DOF RPS revolute prismatic and spherical joints parallel manipulator depicted in Fig. 1 this manipulator a virtual model and an actual one are used here for the experimental evaluation of the dynamic parameter identification process. As can be seen in the figure this parallel manipulator consists of a fixed base and a moving platform interconnected by three RPS .

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