Kinematics of a planar slider-crank linkage in screw form

Abstract

This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

Equilibrium Analysis and Simulation Calculation of Four-Star Type Crank Linkage Mechanism

“…The addition of a gear mechanism can be used to balance the inertia forces generated during the movement of the crank slider. By changing the structural form of the gear mechanism, the purpose of balancing the first-and second-order inertia forces can be achieved [11]. The relevant gear mechanism layout is shown in Figure 5.…”

“…SI1 replaces u = . q in the system of Equation (11), to avoid the pathology of the Jacobi determinant during the solution.…”

Dynamics for a 3-UPU Parallel Robot

“…The kinematics can be simplified by resorting to screw theory, many researchers have applied screw theory in kinematics [24][25][26] and dynamics [27][28][29] in parallel mechanisms.…”

Kinematics of a screw linkage

“…This paper focuses on the kinematics of a screw linkage and proposes an algorithm to investigate the displacement and acceleration with velocities in twist coordinates compared with [13]. A screw linkage is a mechanism each joint of which is a screw one that can be easily reduced to other types of joints.…”

“…Similarly, other types of joints such as spherical and universal ones can also be modelled as the combination of more screw joints in this way. In this regards, all spatial linkages can be generalized as screw ones and this method can be directly generalized to spatial linkages compared with [13]. A linkage is a planar screw linkage when all joint axes have the same direction in space.…”