Valve gear element: eccentric function The function of an eccentric in a steam engine valve gear is to provide ________ motion to the slide valve via the eccentric rod and linkage.

Introduction / Context:
In classic D-slide valve gear, a crankshaft-mounted eccentric acts like an off-center circular cam. Through the eccentric strap and rod, it drives the valve with an approximate sinusoidal displacement to time steam admission and exhaust. Recognizing its kinematic role clarifies valve timing diagrams and setting procedures.

Given Data / Assumptions:

• Eccentric sheave fixed to the rotating crankshaft with an eccentricity e.
• Strap and rod transmit motion to the valve spindle through links.
• Small clearances and rigid links assumed for ideal motion.

Concept / Approach:
The eccentric converts the crankshaft’s rotational motion into reciprocating motion of the slide valve. The valve’s displacement is approximately sinusoidal with amplitude proportional to eccentricity. Advance angle sets the phase relative to the piston, determining lead, cut-off, release, and compression events.

Step-by-Step Solution:
Crank rotates at angular speed ω.Eccentric of radius e generates a harmonic displacement x ≈ e * cos(ωt + φ).Through the rod and links, this displacement translates into back-and-forth motion of the slide valve.Result: reciprocating valve travel that opens and closes ports at the desired times.

Verification / Alternative check:
Valve setting procedures reference eccentric throw (2e) and advance angle; indicator diagrams confirm proper admission and exhaust when reciprocating valve motion is correctly phased.

Why Other Options Are Wrong:
“Rotary” motion is at the crankshaft, not at the valve. Helical or random motions are not applicable. Purely oscillatory with zero translation would not open ports adequately.

Common Pitfalls:
Confusing eccentric with cam; although similar in function, the eccentric produces near-sinusoidal motion rather than bespoke cam profiles.

Final Answer:
reciprocating