The formula to calculate the Number of Joints in a Kinematic Chain when Higher Pair is also Present is:
\[ j = \frac{3 \cdot L_n}{2} - 2 - \frac{h}{2} \]
Number of joints in a kinematic chain is a section of a machine which is used to connect one or more mechanical parts to another. Number of links in a kinematic chain is the total (each part of a machine, which moves relative to some other part) links in a kinematic chain. Number of higher pairs in a kinematic chain is a constraint that requires a curve or surface in the moving body to maintain.
Let's assume the following values:
Using the formula:
\[ j = \frac{3 \cdot 5}{2} - 2 - \frac{2}{2} = 4.5 \]
The Number of Joints in the Kinematic Chain is 4.5.
| Number of Links | Number of Higher Pairs | Number of Joints |
|---|---|---|
| 3 | 2 | 1.500000000000000 |
| 3.1 | 2 | 1.650000000000000 |
| 3.2 | 2 | 1.800000000000001 |
| 3.3 | 2 | 1.950000000000000 |
| 3.4 | 2 | 2.100000000000001 |
| 3.5 | 2 | 2.250000000000001 |
| 3.6 | 2 | 2.400000000000000 |
| 3.7 | 2 | 2.550000000000001 |
| 3.8 | 2 | 2.700000000000001 |
| 3.9 | 2 | 2.850000000000001 |
| 4 | 2 | 3.000000000000002 |
| 4.1 | 2 | 3.150000000000000 |
| 4.2 | 2 | 3.300000000000001 |
| 4.3 | 2 | 3.449999999999999 |
| 4.4 | 2 | 3.600000000000000 |
| 4.5 | 2 | 3.749999999999998 |
| 4.6 | 2 | 3.899999999999999 |
| 4.7 | 2 | 4.049999999999997 |
| 4.8 | 2 | 4.199999999999998 |
| 4.9 | 2 | 4.349999999999996 |
| 5 | 2 | 4.499999999999996 |
| 5.1 | 2 | 4.649999999999995 |
| 5.2 | 2 | 4.799999999999995 |
| 5.3 | 2 | 4.949999999999994 |
| 5.4 | 2 | 5.099999999999994 |
| 5.5 | 2 | 5.249999999999993 |
| 5.6 | 2 | 5.399999999999993 |
| 5.7 | 2 | 5.549999999999992 |
| 5.8 | 2 | 5.699999999999992 |
| 5.9 | 2 | 5.849999999999991 |
| 6 | 2 | 5.999999999999991 |
| 6.1 | 2 | 6.149999999999990 |
| 6.2 | 2 | 6.299999999999990 |
| 6.3 | 2 | 6.449999999999989 |
| 6.4 | 2 | 6.599999999999989 |
| 6.5 | 2 | 6.749999999999988 |
| 6.6 | 2 | 6.899999999999988 |
| 6.7 | 2 | 7.049999999999986 |
| 6.8 | 2 | 7.199999999999987 |
| 6.9 | 2 | 7.349999999999985 |
| 7 | 2 | 7.499999999999986 |