In Klein's construction for reciprocating engine mechanism, the scale of acceleration diagram will be

Explanation:

Klein's Construction:

• It is used to draw the velocity and acceleration diagrams for a single slider crank mechanism.
• The velocity and acceleration of piston of a reciprocating engine mechanism can be determined by the figure given below.

Velocity diagram:

• Draw the configuration diagram OAB for the slider-crank mechanism.
• Draw OI perpendicular to OB and produce BA to meet OI at C. Then the triangle formed, is known as Klein's velocity diagram.
  • Velocity of connecting rod AB, V_BA = ω × AC.
  • Velocity of piston B,VP = V_BO = ω × OC.
  • Velocity of crankpin A, V_AO = ω × OA.

Acceleration diagram:

• With A as centre and AC as radius, draw a circle.
• Locate D as the midpoint of AB.
• With D as centre, and DA as radius, draw a circle to intersect the previously drawn circle at points H and E.
• Join HE intersecting AB at F.
• Produce HE to meet OB at G.
• Then OAFG is Klein's acceleration diagram.
  • Acceleration of piston (Slider B), f_BO = ω² × OG.
  • Tangential acceleration of connecting rod, ft_BA = ω² × FG.
  • Normal acceleration of connecting rod, fn_BA = ω² × AF.
  • Total acceleration of connecting rod, f_BA = ω² × OG.
• Angular acceleration of connecting rod, AB \(\alpha_{AB}=f^{t}_{BA}/AB=ω^{2}\frac{FG}{AB}\;\;\;\;(ccw)\)
• To find the acceleration of any point x in AB, draw a line X-X parallel to OB to intersect at X. Join OX.
• Then, Acceleration of point x, fx = ω² × OX.

Though, we can calculate both velocity and acceleration through Klein's construction but mainly it is used in calculating the linear acceleration of the piston.