A NEW GRAPHICAL METHOD FOR DETERMINING THE ACCELERATION OF CHARACTERISTIC POINTS OF A SPATIAL LINKAGE MECHANISM BASED ON A 3D COMPUTER MODEL

Abstract

In the article, a simple, theoretically based, and sufficiently accurate graphic method for solving practical problems based on a 3D computer model is proposed for determining the relative momentum of the characteristic points of linear space mechanisms relative to each other. The main essence of this method is that the position of the point M moving in the OXYZ coordinate system at any moment is determined by the radius-vector r ̅drawn from the origin of the coordinate O to the point M, and the dependence of r ̅on time differs from each other by ∆φ of the driving point of the mechanism ( ∆φ=0.005÷0.05°) is ensured by constructing a 3D computer model of the plan of states corresponding to three states 〖(φ〗_1=φ_0-∆φ,φ_2=φ_0, φ_3=φ_0+∆φ). If the moving point moves from the state M determined by the radius-vector r ̅at the time τ to the state M_1 determined by the vector r ̅_1 at the time τ_1, the displacement (MM) in the period ∆τ=τ_1-τ is determined by the vector ̅_1 and this vector is the displacement of the point vector, and the ratio of this vector to the corresponding time interval is a vector quantity, ∆τ gives the average speed of the point in value and direction during the time interval. If the point moving with speed v ̅at time τ moves from state M to state M_1 with speed v ̅_1 at time τ_1, then the speed of the point changes by ∆v ̅=v ̅_1-v ̅during ∆τ=τ_1-τ. The vector ∆v ̅can be determined by passing a vector equal to the vector v ̅_1 from point M and constructing a parallelogram with diagonal v ̅_1 and using it to determine the acceleration. Also, on the basis of a three-dimensional computer model, for the first time, the procedure for building the momentum plan was worked out, and using it, a threedimensional computer model of the momentum plan of the five-point space crank-pivot mechanism was built. The correctness of the results obtained by the proposed method was confirmed by comparing them with values calculated by numerical methods, based on the momentum vectors found, by closing the momentum plan of the mechanism at one point.