Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Solution

STEP 0: Pre-Calculation Summary
Formula Used
Displacement = Distance b/w roller centre and nose centre+Distance b/w cam center and nose center-Distance b/w cam center and nose center*cos(Angle turned by cam when roller is at nose top)-sqrt(Distance b/w roller centre and nose centre^2-Distance b/w cam center and nose center^2*(sin(Angle turned by cam when roller is at nose top))^2)
d = L+r-r*cos(θ1)-sqrt(L^2-r^2*(sin(θ1))^2)
This formula uses 3 Functions, 4 Variables
Functions Used
sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Displacement - (Measured in Meter) - Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
Distance b/w roller centre and nose centre - (Measured in Meter) - Distance b/w roller centre and nose centre is a numerical measurement of how far apart objects or points are.
Distance b/w cam center and nose center - (Measured in Meter) - Distance b/w cam center and nose center is a numerical measurement of how far apart objects or points are.
Angle turned by cam when roller is at nose top - (Measured in Radian) - Angle turned by cam when roller is at nose top is the angle turned by the cam measured from the position when the roller is at the top of the nose.
STEP 1: Convert Input(s) to Base Unit
Distance b/w roller centre and nose centre: 8.5 Meter --> 8.5 Meter No Conversion Required
Distance b/w cam center and nose center: 0.012 Meter --> 0.012 Meter No Conversion Required
Angle turned by cam when roller is at nose top: 0.785 Radian --> 0.785 Radian No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = L+r-r*cos(θ1)-sqrt(L^2-r^2*(sin(θ1))^2) --> 8.5+0.012-0.012*cos(0.785)-sqrt(8.5^2-0.012^2*(sin(0.785))^2)
Evaluating ... ...
d = 0.00351557269248737
STEP 3: Convert Result to Output's Unit
0.00351557269248737 Meter --> No Conversion Required
FINAL ANSWER
0.00351557269248737 0.003516 Meter <-- Displacement
(Calculation completed in 00.020 seconds)

Credits

Created by Anshika Arya
National Institute Of Technology (NIT), Hamirpur
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Birsa Institute of Technology (BIT), Sindri
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6 Tangent Cam Calculators

Velocity of Follower of Roller Follower Tangent Cam for Contact with Nose
Go Velocity = Angular velocity of cam*Distance b/w cam center and nose center*(sin(Angle turned by cam when roller is at nose top)+(Distance b/w cam center and nose center*sin(2*Angle turned by cam when roller is at nose top))/(2*sqrt(Distance b/w roller centre and nose centre^2-Distance b/w cam center and nose center^2*(sin(Angle turned by cam when roller is at nose top))^2)))
Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact
Go Displacement = Distance b/w roller centre and nose centre+Distance b/w cam center and nose center-Distance b/w cam center and nose center*cos(Angle turned by cam when roller is at nose top)-sqrt(Distance b/w roller centre and nose centre^2-Distance b/w cam center and nose center^2*(sin(Angle turned by cam when roller is at nose top))^2)
Velocity of Follower for Roller Follower Tangent Cam if Contact is with Straight Flanks
Go Velocity = Angular velocity of cam*(Radius of the base circle+Radius of Roller)*sin(Angle turned by cam from beginning of roller)/((cos(Angle turned by cam from beginning of roller))^2)
Displacement of Needle for Tangent Cam with Needle-Bearing Follower
Go Displacement = (Radius of the base circle+Radius of Roller)*((1-cos(Angle turned by cam from beginning of roller))/cos(Angle turned by cam from beginning of roller))
Condition for Contact of Roller if Straight Flank Merges into Nose Tangent Cam with Roller Follower
Go Angle turned by cam when roller is at nose top = Angle of ascent-Angle turned by the cam for contact of roller
Distance between Roller Center and Nose Center of Tangent Cam with Roller Follower
Go Distance b/w roller centre and nose centre = Radius of Roller+Radius of Nose

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact Formula

Displacement = Distance b/w roller centre and nose centre+Distance b/w cam center and nose center-Distance b/w cam center and nose center*cos(Angle turned by cam when roller is at nose top)-sqrt(Distance b/w roller centre and nose centre^2-Distance b/w cam center and nose center^2*(sin(Angle turned by cam when roller is at nose top))^2)
d = L+r-r*cos(θ1)-sqrt(L^2-r^2*(sin(θ1))^2)

What is tangent cam with reciprocating roller follower?

Tangent cam with reciprocating followers is an example of cams with specified contours. Tangent cams are symmetric about the centerline of the camshaft and hence they fall into a category of cams with specified contours. Tangent cams are symmetrical about the centerline of the camshaft.

How to Calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?

Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact calculator uses Displacement = Distance b/w roller centre and nose centre+Distance b/w cam center and nose center-Distance b/w cam center and nose center*cos(Angle turned by cam when roller is at nose top)-sqrt(Distance b/w roller centre and nose centre^2-Distance b/w cam center and nose center^2*(sin(Angle turned by cam when roller is at nose top))^2) to calculate the Displacement, The Displacement of roller of tangent cam with roller follower, when there's nose contact formula is defined when an object moves relative to a reference frame. Displacement is denoted by d symbol.

How to calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact using this online calculator? To use this online calculator for Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact, enter Distance b/w roller centre and nose centre (L), Distance b/w cam center and nose center (r) & Angle turned by cam when roller is at nose top 1) and hit the calculate button. Here is how the Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact calculation can be explained with given input values -> 0.003516 = 8.5+0.012-0.012*cos(0.785)-sqrt(8.5^2-0.012^2*(sin(0.785))^2).

FAQ

What is Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?
The Displacement of roller of tangent cam with roller follower, when there's nose contact formula is defined when an object moves relative to a reference frame and is represented as d = L+r-r*cos(θ1)-sqrt(L^2-r^2*(sin(θ1))^2) or Displacement = Distance b/w roller centre and nose centre+Distance b/w cam center and nose center-Distance b/w cam center and nose center*cos(Angle turned by cam when roller is at nose top)-sqrt(Distance b/w roller centre and nose centre^2-Distance b/w cam center and nose center^2*(sin(Angle turned by cam when roller is at nose top))^2). Distance b/w roller centre and nose centre is a numerical measurement of how far apart objects or points are, Distance b/w cam center and nose center is a numerical measurement of how far apart objects or points are & Angle turned by cam when roller is at nose top is the angle turned by the cam measured from the position when the roller is at the top of the nose.
How to calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact?
The Displacement of roller of tangent cam with roller follower, when there's nose contact formula is defined when an object moves relative to a reference frame is calculated using Displacement = Distance b/w roller centre and nose centre+Distance b/w cam center and nose center-Distance b/w cam center and nose center*cos(Angle turned by cam when roller is at nose top)-sqrt(Distance b/w roller centre and nose centre^2-Distance b/w cam center and nose center^2*(sin(Angle turned by cam when roller is at nose top))^2). To calculate Displacement of Roller of Tangent Cam with Roller Follower, when there's Nose Contact, you need Distance b/w roller centre and nose centre (L), Distance b/w cam center and nose center (r) & Angle turned by cam when roller is at nose top 1). With our tool, you need to enter the respective value for Distance b/w roller centre and nose centre, Distance b/w cam center and nose center & Angle turned by cam when roller is at nose top and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Displacement?
In this formula, Displacement uses Distance b/w roller centre and nose centre, Distance b/w cam center and nose center & Angle turned by cam when roller is at nose top. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Displacement = (Radius of the base circle+Radius of Roller)*((1-cos(Angle turned by cam from beginning of roller))/cos(Angle turned by cam from beginning of roller))
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