In this paper, according to high load capacity and rather large workspace characteristics of cable driven robots (CDRs), maximum dynamic load carrying capacity (DLCC) between two given end points in the workspace along with optimal trajectory is obtained. In order to find DLCC of CDRs, joint actuator torque and workspace of the robot constraints concerning to non-negative tension in cables are considered. The problem is formulated as a trajectory optimization problem, which is fundamentally a constrained nonlinear optimization problem. Then the iterative linear programming (ILP) method is used to solve the optimization problem. Finally, a numerical example involving a 6 DOF CDR is presented and results are discussed.

This paper presents the investigation of general formulation and numerical solution of the dynamic load carrying capacity (DLCC) of flexible link manipulator. The proposed method is based on open loop optimal control problem. A two point boundary value problem (TPBVP) is taken from the Pontryagin's minimum principle. The indirect approach is employed to derive optimality conditions. The system’s dynamics equation of motion is obtained from Gibbs-Appell (G-A) formulation and assumed mode method (AMM). Elastic properties of the links are modeled according to the assumption of Timoshenko beam theory (TBT) and its associated mode shapes. As TBT is more accurate compared with the Euler-Bernoulli beam theory, it is utilized for mathematical modeling of flexible links. The main contribution of the paper is to calculate the maximum allowable load of a flexible link robot while an optimal trajectory is provided. Finally, the result of the simulation and experimental platform are compared for a two-link flexible arm to verify the introduced technique. The efficiency of the proposed method is illustrated by performing some simulation studies on the IUST flexible link manipulator. Simulation and experimental results confirm the validity of the claimed capability for controlling point-to-point motion of the proposed method and its application toward DLCC calculation.

In this paper, optimal trajectory planning of flexible joint manipulator in point-to-point motion is presented in which besides the determining the maximum load carrying capacity, the vibration amplitude is also reduced. The solution method is on the base of the indirect solution of optimal control problem. For this purpose, an appropriate objective function is defined, dynamic equations are derived in state space form, Hamiltonian function is developed and necessary optimality conditions are obtained by using the Pontryagin maximum principle. In order to reduce the vibration of the end effector during the path, an appropriate state variables are defined and the control law is improved to omit the suddenly variation in applied torque. Then, in order to illustrate the power and efficiency of the proposed method, a number of simulation tests are performed for a two-link manipulator. To this end, after deriving the equation in details, two simulations are performed. In the first case, determining the maximum load without considering the vibration is solved, in the second simulation, optimal trajectory with maximum load and minimum vibration is obtained. Finally discussions on the obtained results are presented.

Design of structures under impulsive loads is usually accomplished through nonlinear inelastic dynamic analysis followed by implementing acceptance criteria of the nonlinear analysis specified in design codes. Nonlinear dynamic analyses inherently consist of convergence and computational effort problems. In this research, the capacity modification factors of steel moment-resisting frames' members are calculated in order to simplify the design of the structures subjected to impulsive loading. Capacity modification factors are proposed for different loading conditions that provide a design procedure to perform the linear dynamic analysis, instead of the time consuming nonlinear dynamic analysis. Herein, an algorithm is proposed to calculate the capacity modification factors as an inverse problem. Firstly, a designed structure is nonlinearly analyzed under impulsive load; then, the structure is checked whether the acceptance criteria are satisfied. For a steel frame structure, story drifts should be restricted to 1/14 of story height; a chord rotation of the members should be restricted to 2 degree. Secondly, if the acceptance criteria are satisfied with minimal tolerance, the structure with the accepted properties is linearly analyzed; otherwise, the structure should be redesigned to reach the desirable condition. Results of the linear analysis are checked by ASCE41-13 acceptance criteria for the linear analyses. These acceptance criteria control demand and capacity moments for a beam, demand and capacity axial force, and moment interaction of columns such that the capacity modification factors are involved in both of them as unknown variables. Thirdly, the capacity modification factors are calculated for each member using the formulations presented for the acceptance criteria of the linear analyses. Here, a portal frame is used as a representative of entire moment-resisting frame to evaluate different types of loading (magnitude and condition). Three loading conditions are defined to mobilize three deformation modes consisting of lateral, gravity, and lateral-gravity modes. The first mode includes laterally distributed and concentrated loads on the left column and downward loads on the beam; the second mode only includes downward loads on the beam; the third mode only includes laterally distributed and concentrated loads on the left column. Finally, many capacity modification factors are attained for every member of a steel moment-resisting frame. These data should be processed by statistical relations to obtainfirm results for the main members of the structure. The capacity modification factors are herein calculated for four member groups including roof beams, internal beams, external columns, and internal columns. Results demonstrate that external columns exposed to direct impulsive loads are not ductile as much as internal columns. In other words, internal columns can go beyond the linear limits more than external ones. The roof beams have lower ductility than the internal beams. The reason is the directly imposed impulsive load on their span. Therefore, the calculated factors can be used for new acceptance criteria that need linear dynamic analysis. The proposed procedure leads to avoidance of performing the complicated nonlinear analysis under impulsive loading, while acceptance criteria of nonlinear analyses are satisfied by employing linear dynamic analysis. In addition, this development reduces computational efforts and can be extended for future design codes.