We suggest a method for solving a boundary value problem for ordinary differential equations with boundary conditions in the presence of state and integral constraints. The method is based on the embedding principle, which permits one to reduce the original boundary value problem to a special optimal control problem with the use of the general solution of a Fredholm integral equation of the first kind.
STATEMENT OF THE PROBLEMConsider the boundary value probleṁwith the boundary conditionsthe phase constraintsand the integral constraintsHere A(t) and B(t) are given n × n and n × m matrices, respectively, with piecewise continuous entries, μ(t), t ∈ I, is a given n-dimensional vector function with piecewise continuous components, f (x, t) is an m-dimensional vector function that is jointly continuous with respect to the variables (x, t) ∈ R n × I and satisfies the conditionsand S is a given convex closed set. The function F (x, t) = (F 1 (x, t), . . . , F r (x, t)), t ∈ I, is an r-dimensional jointly continuous vector function, and γ(t) = (γ 1 (t), . . . , γ r (t)) and δ(t) = (δ 1 (t), . . . , δ r (t)), t ∈ I, are given continuous functions.149
In this paper the methods of structural synthesis and direct kinematics of six-DOF three-limbed parallel manipulator (PM) are presented. This PM is formed by connection of a mobile platform with a base by three dyads with cylindrical joints. Constant and variable parameters characterizing geometry of links and relative motions of elements of joints are defined. Direct kinematics of the PM is solved by iterative method.
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