<p>Triangular and trapezoidal velocity profiles are widely used in industrial servo-controlled motion systems because of their intuitive phase-based timing structure and compatibility with commercial motion controllers. However, their classical piecewise formulations contain acceleration discontinuities at phase transitions, which may cause impulsive jerk and reduce the reliability of analytical dynamic evaluation in multibody dynamic simulations. Existing smooth trajectory-planning methods can overcome this limitation, but they often modify the original industrial timing semantics or require numerical construction. This study proposes a polynomial standardization framework for reconstructing industrial triangular and symmetric one-third trapezoidal velocity profiles in closed analytical form. The triangular profile is reformulated using a normalized fifth-order displacement polynomial, while the symmetric one-third trapezoidal profile retains its constant-velocity phase and replaces the acceleration and deceleration phases with polynomial-shaped boundary phases. The resulting motion laws provide closed-form displacement, velocity, acceleration, and feasible duration expressions under prescribed velocity and acceleration limits. The proposed profiles are evaluated through a computer-aided-design-based multibody dynamic simulation of a gantry robot integrated with a transport system. The results show that the standardized symmetric one-third trapezoidal profile requires a longer cycle time, but reduces the root-mean-square velocity, acceleration, and vertical actuator driving force compared with the standardized triangular profile. However, the peak-to-peak vertical driving-force envelope remains nearly unchanged. These findings show that the symmetric one-third trapezoidal profile mainly reduces time-averaged dynamic intensity, whereas the triangular profile remains advantageous when shorter cycle time is required.</p>